To be honest there should be events during the colonisation process that change it to your culture and religion, with the MTTH increased or decreased based on native size, ferocity and aggressiveness.
Things like native population over 4000-5000 should be near impossible to convert naturally and you must spend the diplo points to convert it if you really want.
Uninhabited places should obviously be your religion and culture.
Then again I feel like colonisation needs a complete rework.
Good idea... but then, everyone would kill all the natives...
But I think colonization has always been to easy in Europa Universalis:
Changing culture through colonization should only be possible through events or investment of diplo points, and getting rid of the natives should cost more MIL points, and it should be made impossible to sweep more than 5000 natives in one strike.
Also, it's unrealistic that the troops "waking" the natives get the terrain bonus. The natives should get the terrain bonus because, y'know, they've always been there.
Also, a colonial nation owning a lot of native culture provinces should see new culture appear: for example, iberian CN should get latino, mexican or colombian cultures, french CN, creole (even if it comes more from the slaves than the natives...) or quebecois culture.