Here's a thought. Perhaps Human History had always had these deaths, it's just the Singularities were always the cause. You're assuming a butterfly effect, but Gilgamesh specifically stated that history tries to make the deaths make sense historically, so what if there's no change to the timeline because the Singularities effects were accounted for from the beginning.
Like for instance, the thousands of people who died from the fog in Real History? What if that was caused by the Singularity being fit into real history and the thousands who died was part of the death toll of the Singularity.
Plus, you're also assuming that these people all died at the same time, there's always the possibility that they're dying at different points, and given how people tended to die young in the past (even as close to the present period as say London), there's no real difference to history, since they'd be more likely to die from accidents or illness regardless. That would explain why the destruction of Uruk as a nation-state would destroy Human History, instead of all the people. There's enough of a gap in there to allow them to have children themselves and raise them before they all pass on one at a time, instead of all at once which would be more devastating.
You might argue that that's not how it was explained, but all Gilgamesh said was that everything we did mattered, because the Singularity does affect Human History. That every man we saved in the singularity is a man we saved in real history too, and that history adjusts everything to fit the grand scheme of things. (so say George Washington was killed, History would leave him alive to live out his life, before eventually killing him off when his fate no longer matters to history.)
Because that makes no fucking sense for an urban fantasy world that's supposed to look like ours on the surface? You can actually hand wave plenty of stuff away by saying, 'this world looks like ours so you assumed these historical events
mostly lined up, but you're actually wrong, I never said Rome didn't have an extra civil war during Nero's reign.' That actually works for some things, but doesn't actually work for most of Grand Order. It might work for the example I just used, but it doesn't work for much else. Chaldea is an organization of Mages tasked with safeguarding history and they find all these events surprising. If there were massive unexplained dips in life expectancy around the times of singularities then characters really should have noted that. They're never surprised that something is the reason for a lot of deaths, they're surprised the deaths are happening period. The Orleans singularity is introduced as the beginning of a lull in the Hundred years war after Joan of Arc's execution, not a lull that was mysteriously more deadly than all the 'hot' periods of the war put together. There's never a 'huh I always thought it was weird that so many accomplished mages also died around the time of the Great Fog, I guess we know why now' moment. I could give you the Singularity being the real cause of muggle deaths from that time since it matches up almost perfectly, but it's the only Singularity that does match up that neatly, so I can't buy it as an explanation for the whole. So at the very least, the Singularities and their effects are aberrations from the point of view of Chaldea's original timeline.
People just not dieing all at once as an explanation for why it doesn't get noticed is kind of weird. Here's why:
Gilgamesh: Naive fool! You thought the dead would simply come back? If you didn't save them then they're gone.
MC: How the fuck did I save history then? Everything should be fucked by now if that's the case.
Gilgamesh: Oh I meant they will die. They might die immediately or they might die 20 years after the singularity that killed them.
MC: So they come back, they might even live out most of their natural lives.
Gilgamesh: They're dead, but not necessarily immediately.
MC: Isn't that just the human condition? Dieing 20 years after the singularity after they've served their historical purpose and raised kids sure doesn't sound like 'people die when they are killed.'
Note: I haven't gotten to said conversation yet, not meant to be an accurate representation.
But the main offenders are France and America. We actually can say French history is mostly supposed to match up to ours post-singularity because Marie and Napoleon exist. Heck, history actually got the genders of all the French Heroic Spirits that I can think of right, so history is really batting a thousand there. So like half the French population died after Joan of Arc did, but French history still followed all the same beats it did in the real world? Fuck that.
And we know that America exists in the Nasuverse, we know several heroic spirits that match up with history as we know it, we know World War 2 happened, and we even know that Bill fucking Clinton becomes president and that Iskandar saw him as his greatest potential rival for world domination if he got his wish. Which really doesn't square with the east coast (read: all of America) all dieing less than a decade after the country is founded. I don't care how much history tries to adjust things, France and America are too fucking big.
In the end it's just a pointlessly convoluted retcon that supposedly gives things more stakes, but pretty much the only non-Servant/Chaldea death that's not statistic is Siduri. And one of the above comments mentioned that people getting converted into Lahmus got fixed by restoring history, so the one
meaningful (permanent?) death the story gave us got retconned out from under the stupid retcon that would have made it matter.
Since I haven't actually reached the conversation yet, I have to ask if the common interpretation is actually right. Are we sure Gilgamesh meant 'People die when they are killed' rather than 'It's never wrong to save someone' or 'Of course it never happened, but why on earth should that mean it's not real Harry?'
Edit: Finally, at the end of this monster, I'd like to apologize for creating it. You did not deserve this stream of barely coherent word vomit.