The main problem with this is how to implement it without making it unfun. How would you make it an engaging, challenging mechanic to fight against, instead of just a frustrating one?
(I'm actually asking; I have no idea)
This one is hard, even more since we dont get paid to find the solution for it.
But here are some way (not best or only option, just few ideas):
Cultures and relegion: Conversion dont go in one big chunk per province, but smaller steps (like one pop/development), some are automated (coring gives you some your cultures pop, since you send your own nobles and a few local convert to the new regime) some are forced (conversion action) and some are event based, so a 20+ development province will take dacedas to fully convert, if you press the issue, or even centuries if you wait for the free options, this also gives chance for mixed situations, a province which changed ownership multiple times could end up with several religion and cultures.
Time: Implement timedelay, yes, your DoW against the natives will arrive 6 month later than issued, add territories or theaters, where the governor can start local war against the nativas or locals, and the locals can declare war on the theater, which will not be known to the palyer for some time.
Size: Add true corruption and governors, the east india company did not increaed the incoma of their country, but decreased the governing problem of those areas. Far away areas and territories are not effective or beyond some point even profitable.
Internal integritiy: Take ideas from CK2, the council needs to agree in some stuff, when the noble in the council will only agree for the war, if you have a claim for it, then claim creation is not a stupid system, but a nice option, when the burgers agree only if it seems profitable (COT and so), then blobbing has a reason, instead painting the map, when the clergy wont agree on samerelegion, then it is more important to choose your side in the reformation, and you get a reason for colonization, since the catholic south has no good option to expand othewise.