Currently, the game has 3 primary layers to develop your yields and infrastructure.
- The main planet screen, using manu to develop buildings.
- Your stardock, providing supply ships and projects using military.
- Your population, providing yields through specialists.
The first two work well together, and both can support each other (supply ships providing extra manu for buildings, buildings providing more military yields for faster ships). They also both tend to escalate as the game goes, turn 1 it might take 8 turns to build a manu district, as the planet fills up, maybe only 2-3.
Growth works mostly the opposite. The more people I have, the slower it becomes to get more. Take this screenshot as an example, this is about as good as it gets. I have an insanely good medical facility (+90% growth) and a number of other growth bonuses. Yet its still taking me over 30 turns to get more pop, at a time when I can build buildings in 1-2 turns.
Now if specialists were really powerful, this could be justified. But most of the time, specialists grant yields in the 5-9% range, which when you factor in adjacencies is about what the various buildings provide (buildings in clusters can often provide even more).
Further, if pop didn't require anything, than the slow times could also be understood. But pop requires tile utilization in the form of hospitals (to have any workable growth), housing districts, and the need for food.
Long story short, I think growth requires at higher pops needs to be adjusted. It shouldn't take significantly longer to get pop 15 than it takes pop 10... or if that needs to be curbed, perhaps increase the food requirements or something. But if I am willing to put in the work to have a high pop planet, I should be able to get there. Otherwise, a pop 15ish world is just untenable using normal methods, which leads me to my next point.
There is a subversive way you can ratchet up the growth on a planet. Have other worlds with low population send colony ships. This is where the growth rates get really weird. My little pop 3 planet with high manu can churn out pop like its going out of style, and grow a world 20x faster than it can do through just normal growth. That alone should suggest that growth has a bit of a problem.