All sorts of things. Off the top of my head, in addition to straight up income gains (or reduced expenses, which work out to being basically the same) it could open up an event chain like the Grand Cothon did for trading ships that has narrative effects but not necessarily show up in the mechanics or it could be that taking firmer reign over the Treasury will open up statistics like how much of our population is barbaroi and allow for more subtle and more effective efforts to track/manage integration.
Regardless, the point is that making an argument that "it'll give at least 4 Silver" just doesn't work. We can't say that it'll be worth a certain amount of money or not because literally the only thing we know about it is the name, and relying on it producing a given amount is just asking to get bitten on the ass.
We also won't have to deal with 50 thousand natives to fight, so the lack of native allies is completely irrelevant. There is no scenario in which we might plausibly come up against a force that has the same amount of numbers we do.
Trying to bring up whether or not our army would break if we were outnumbered twice over simply doesn't matter. At all.
1. There are 2 competing plans. One of them cuts 60% of our income and triples the amount of professional troops the Crown contributes to the armed forces while the other one cuts 20% of our income to increase the amount of professional troops by a third. Arguing that the less extreme plan is unreasonable because it doesn't do enough falls flat because the only alternative that has been presented is a plan that does way too much.
2. No, I didn't take any possible earnings into account - for the simple reason that you weren't including it in your projections and I stuck to comparing apples with apples. Which is also why including stuff like assumptions about how much the Treasury would earn is a bad idea. Including stuff that isn't hard math into your projections moves them from being projections into wishful thinking.
Regardless, the point remains that wildly overspending on our military will cost more in lost income then it'll gain in ephemeral benefits - this remains the same whether you take into account the effect of conquered territories on overall income or not. How much money can be gained from conquering somebody relies more on how much money they have than how much force is applied taking it from them.
3. Having more full-time troops is almost completely unrelated to how many settlements we can seize. Having 4k troops out of 22k troops be slightly more or slightly less effective matters a lot less than having 22k troops compared to 10-15k, the tactical/strategic skill of each side, and chance. Chance and tactical/strategic skill are out of our hands (which makes them identical as far as planning is concerned), as are the final troop numbers the Tuscarora will have. The total amount of troops remains the same in both plans, which means that all 3 major factors are fixed - fiddling with how effective a sixth of the army will be is by definition a marginal difference in comparison.
Therefore, it's better to attack a place and see how much it gains us before spending on Allagia until we have enough to pacify it than to hire Allagia for pacifying a place before we take it. It is the simple difference between earning money and then spending it versus spending money and then trying to earn it. One of them leads to success, while the other leads to financial hot water.
4. No, that's not how it works. We don't have a limit on how many bodies we can recruit, we have a limit on how much of our population can be mobilized without damaging the economy. The cap on militia is directly proportional to our population level. If we go into battle and lose 5k militia, we can continue recruiting until we hit the cap - only the cap would be slightly less to account for having 5k less total population having done some damage to our overall economy.
Numerically, if we have 200k people and can support 10k troops, then going into battle and losing 5k troops means we'd now have 195k people and could support 9.75k troops, which means that even though no more troops could be recruited before the war after the war 4.75k troops could be recruited.
Losing 3% of our population isn't going to cripple our military for a generation.
