In reality, the decline in population was spread out over several centuries.
Yes. I gather it finally bottomed out late in the 19th century in North America, but I suppose it did so some centuries before in places like Mexico and Peru. So the overall process was indeed spread out over many centuries, and if it were to somehow happen all at once which it did not for reasons discussed below, it would have taken maybe a couple centuries less to bottom out.
It could be unnoticeable from one generation to another.
Well, you seem to be ignoring the punctuated nature of it. The thing is the Americas were not as closely knit with trade networks, fewer societies were as dependent on them, and a spreading Eurasian plague would tend to break the trade chain the disease moved along, particularly after devastating great population centers and radiating out to where trade and complex integrated societies were less prevalent. This meant that people who were indeed indirectly connected to say Mexico while living in say Missouri simply stopped seeing trade goods filtering in from Mexico--until some European explorer (DeSoto say) showed up in the region with disease-bearing pigs going feral and getting the diseases into the wildlife too--then that formerly connected region that became an isolated region would become a plague region.
So, for reasons having little to do directly with how human populations resist disease when these are in fact introduced, relating instead to why pre-agricultural civilizations did not probably suffer epidemic or endemic former epidemic diseases at all, disruption of a major population center would not necessarily propagate to other population centers. But here you seem to have substituted for the reality, which is that regions would be sheltered from exposure at all and then suddenly be exposed and experience quite rapid and large scale collapse, an oversimplified assumption the exposure spreads and people succumb at a rate averaged out between 1492 and say 1900. That gives a misleading picture of the dynamic. The "Seven Cities of Gold" game imagery in which a conquistador's mere appearance causes Native people to pop like soap bubbles is equally cartoonish of course, but it does not help to replace an oversensationalizing cartoon with a soothing understating cartoon. We have to look at what really happened.
An important component was that disease vectors were constantly re-introduced, as new colonists and their livestock arrived. Decade after decade, and making it more difficult to develop immunity.
If new colonists were introducing the same diseases, even mutated strains of the same diseases, over and over, you would be describing the opposite of how human immunity works. If you have a population already exposed to smallpox version A, and then ten times as many conquistadors and colonists show up with smallpox B, the remnant population surviving A ought to do relatively better against B despite the more intense exposure--the trends should offset each other, not saying that a sufficiently large invasion would not overwhelm even a surviving population quite heavily immunized by recent (past decade or so) exposure to the prior strain of germ.
But when you bear in mind that Eurasia was a damn cesspool of dozens or hundreds of separate diseases and each wave of colonization was liable to add a new one never seen in the New World before, so we are introducing bugs the Native remnant had never encountered at all, and that immunity tends to be specific to pathogens rather than some spectrum generic "disease resistance," then yes, this modified form of what you are saying does apply.
The decline in population was not due to diesease alone, but in combination with colonialism, that destroyed native societies and made them more vulnerable to the dieseases.
Strongly agreed to this, but I think you are still understating the degree to which the high novelty of infectious spreading disease to New World population skewed the outcome much worse against them. Europeans were trying to colonize places in the Old World too, in Africa and India--and they did accomplish devastating transformations, but these zones did not suffer the sort of demographic collapses the New World did. Massive diebacks, lost civilizations...yes. But magnitude matters here. We simply do not know how much less bad it would have been for various peoples if the Europeans had been behaving in a benign, considerate fashion.
But one thing we do know is, some of the known cases of extensive levels of development going poof to the point that in later centuries, it was entirely unclear to European descended people that extensive cultivation and specialization had been a real thing among the Native peoples did happen behind European backs as it were--one expedition did lasting and unintentional damage that acted as a slow fuse destroying people who were pretty vigorous when they were showing the European explorer-culprits the door.
One of these I have in mind is the various peoples of the Mississippi valley system, the culprit being DeSoto. He came, he trekked halfway up the river to Missouri or so, recorded all sorts of observations of rather populous and developed civilization, moved back to base and died, and neither his Spanish patrons nor any other European power followed up for a couple centuries. The next bunch of Europeans to take a good look at the region were associated with New France, missionaries and functionaries of the fur trade, and they saw what looked like primitive wilderness to them.
Another is something broadly similar only with even later and more peripheral European follow up later, in the Amazon river system. Again we had a bunch of Spanish backed explorer/conquistadores who reported being hotly pursued by legions of quite angry Native people, large towns, complex cultivation arrangements, etc, and managed to get the hell out with most of their skins largely intact to tell the tale. But either because these reports discouraged follow up or because they failed to report any resources to exploit the Spanish or rival Europeans pirating copies of these reports were keenly interested in, the upper river stretches were left largely alone for centuries, and again, when European-Atlantic metaculture zone people showed up to explore again, they saw nothing but "wilderness." But we know today, from satellite imagery leading to specific digs, that in fact the old Conquistadors were not lying about the huge populations and developed elaborate structures they reported. We know this now anyway, but back in the 1980s scholarship was blissfully unaware and all the text reported the Amazon as a primordial jungle.
So--while clearly the massacres and exploitations of conquerors bent on plunder and self-glorification were contributing factors in the collapse of those New World peoples that the conquistadors and their successors and rivals battened on to, and they witnessed the demographic collapse happening right before their pitiless (for the most part, the occasional De Casas to the contrary) eyes, it is also clear that devastation down to the level of the survivors relying on gathering and hunting exclusively, with the very low population density associated with that, without any European exploiters to keep kicking and pushing and stabbing into the bargain.
Again, it is wrong to exaggerate the vulnerability perhaps, but on the whole I think wronger to shrug it off and suggest that it was all the same as if these same diseases had been introduced in the Old World (to populations on the trade routes that is--isolated people there might be almost as bad off as Native Americans generally).
I won't speculate in how bad it would be in the Old World, it would have consequences akin to the Black Plague and the Justinian Plague, only on steroids, but not as bad as in the New World.
I don't think it is possible to have a symmetrical Columbian disease exchange as the OP describes it; we could have a situation where the New World has pretty much the same degree of diversity of nasty diseases as the Old World does, but the outcome would be a moderate intensification of the general background level of disease in both "worlds" quickly (well, over a century or so) stabilizing toward pretty much the same level as OTL. No massive dieback in the New World despite the total novelty of the particular pathogens, and none in the Old World either. That, given a radically different pattern of development in the New World, might be possible.
Having the Old World suffer the sorts of massive diebacks I fear your post tends to downplay as a real thing by saying, in caricature form anyway "it was all just exploitive colonialism," which ignores the evidence of major regional collapses without sustained European presence, no I don't think that can happen at all, for reasons I intend to say more about soon.
And the New World, ironically, would not be as bad as OTL New World, because it would not be colonised as hard when the colonizers are literally plagued by massive epidemics.
The New World might suffer badly despite the absence of the major demographic collapse additionally due to disease being quite novel here, just as the peoples of say Indonesia or West Africa did. And while I suppose a whole continental system's worth of totally novel diseases in Europe might knock the Europeans back for a century or so, and thus delay the mechanisms producing our modern era of global history, that is all that will happen. Perhaps Europe might be so hard hit by some particular bugs that some other society elsewhere in the world invents modern capitalism thus aborted in Europe, but I think if that will be in the cards it would require a more massive devastation of Europe than I think possible, and require really long periods of time for some other zone to cultivate the perfect storm of features that tipped Europe first to capitalism OTL. And once some region goes capitalist, I think it is pretty much destined to conquer the world. Without the sorts of windfalls the depopulated New World gave Europe ready to hand, elements of the process will be protracted, so between say a century or two delay in getting the global ball rolling and a general slowdown of processes that happened OTL between 1500 and 1800 adding say another two or three centuries, we might be some 400 years behind, offset by other peoples getting more effectively and with more global balance into the game in various niches the slower European expansion leaves open for them--more Japans basically, insinuating themselves in opportunistically. So call it 200-300 years delay overall, call it 250 for an average, and we have the clock back to the American Revolutionary period or something like it happening now, except not that because the colonies would be far older if slower spreading...but anyway something along the lines of the British-north European industrial revolution in tandem with something like the French political revolution would be ahead of us in the 21st century instead of most of 2 centuries behind us.
At this rate we might hit the next glaciation before global warming achieves much momentum.