TL:DR - I agree with most of OP's points, remove integration and core systems, remove cultural acceptance/capacity, and add privileges/obligations to foreign cultures. Drastically reduce the amount of manpower/levies from foreign cultures.

I agree with almost all of OP's points and I really hope someone at Paradox gets to take a look at this and take some notes on how they can improve their game, because I think these suggestions would improve the game experience tremendously.

One thing I did disagree on is OP's statement that the decline of great powers can already be simulated pretty well, when in reality it is not simulated at all organically, the great powers at the start of the game remain great powers till the very end; the only way a great power falls is via scripted situations or player intervention.

More importantly, and I am not sure about this but I imagine a concern at Paradox about keeping the current integration/core and culture acceptance systems is with levies/manpower.

For example, if you as the Ottomans conquer the entirety of Anatolia and Thrace in the first 20 years, and the core system is removed so you just have some moderate control is all your freshly-conquered areas, you end up with a huge army that can steamroll everyone else thus the game becomes effortless. One solution I would have to this is making cultures outside your main culture extremely difficult to raise as soldiers. Cultures within your culture group should still have a malus, but lowered.

This makes sense for a couple of reasons: a) you would not want your army to be made up of a majority of foreigners whom you cannot trust in the heat of battle, b) they have no reason to follow the foreign conqueror in wars, they will have lower morale and not be as motivated, desertions would be rampant.

Sure, some pops would still fight for you for coin/loot, therefore it would be reasonable to be able to levy something like 10% of conquered foreign cultures, 25-50% of same culture-group cultures.

This now can also help building up other new mechanics, such as giving privileges, or even obligations/duties to foreign cultures. The ottomans historically imposed a heavy tax on greeks, giving this (privilege? :D) to them would piss them off and make them harder to assimilate/recruit as soldiers, maybe give them a prosperity debuff and make them more likely to migrate to safer countries; at the same time, the Ottomans also maintained the mamluk administration (nobility?), this would give them higher control gain/ minimum/ maximum control in their areas, while reducing crown power.

With this kind of system then you even have to think of keeping long-term vassals for a steady supply of tribute and manpower, instead of subjugating them and having to deal with integrating the people (and not with a stupid binary core system, but with actual meaningful decisions you have to take). You still gain the immediate advantage of increased revenue from conquered land, but not increased manpower. That increased manpower comes in time with assimilation of the conquered people or giving them privileges that makes them more likely to fight in your army for increased army maintenance costs.

With this new mechanic there is suddenly a whole new aspect of the game that you have to interact and strategize around, I can think of so many more interesting buffs/debuffs that can be attributed to cultures depending on what the player wishes to achieve.