Considering what you are asking for is bsically what FE:LH uses, I am guessing they made a conscious decision not to go the same rout for GCIII. I personally would like to see some more ways to boost organic growth rates, but I'm not sure that the connection between excess food and growth is a great mechanic for this game.

What is FE:LH?

Edit: oh, I thought only about space 4X games, you mean Fallen Enchantress:Legendary Heroes. While I played FE, I didn't play LH and can't remember their mechanics anyway ...

How?  Obviously new colony would grow slower and host would replenish slower but early on pop growth is very slow anyway.  Typically i only pull 0.5 pop from host to colonize.  Not sure how this nerfs C spam unless you make a low starting pop ( e.g. 0.5) grow sooo slow, like 20 vs 5 to grow to 1, that its a really bad move. Thus forcing you to pull 2-2.5 pop from home limiting you to only ~5-7 planets to grab in the initial rush.    ..... Oh, guess that would do it

Uh.  Yeah.  I think we can throw real science straight out the window on this aspect of GC3.

I think it would have made sense to go at it from the other direction: first figure out growth globally.  Then in a separate process you can distribute that growth to the colonies.  The population itself has to be the major factor.

A typical scenario on a given week, let's say the population might grow by 1.2m.  This the game would need to distribute among shall we say, six planets, of people-size 3, 3, 1, 8, 9 and 12.  And the amounts might wind up being +.17, +.19, +.03, +.24, +.21, +.36. So a comparable sized population might have their planets show comparable net growth, but you see how it suddenly begins to make more sense - your colony that you settled with that empty colony pod, and is all descended essentially from a single man, the bimboish captain of your vessel perhaps, doesn't want to grow so fast!

How about combining population growth and immigration but so that it's actual real immigration what's happening while also keeping it automatic and very simple?

The current +0.1/turn is a good rate for new settlements from the game-mechanics point-of-view. It gives a reasonable rate to get the production going. For small populations on new worlds it also must come mostly from immigration or you'd get a ridiculous birth rate.

Reasonable pop growth: If 1 turn is a week then let's say pop growth is +0.1%/turn (meaning +5.3%/year).

In any world that has reached its pop cap those +0.1% want to emigrate elsewhere. This is the immigration source pop.

In any world that has not reached it pop cap the +0.1% goes to local pop growth. If this is greater than 0.1 billion or greater than what's needed to reach the pop cap the remainder want to emigrate elsewhere adding to the immigration source pop. (A rare occurrence as you'd need a 100b pop world for this but let's have this case, too, as you may want to mod the turn to represent a month or even a year and thus want to increase the pop growth rate.)

Any world where +0.1% gives less than 0.1 billion and has not reached its pop cap is a target world for immigration and it can receive as many immigrants as is needed to fill up that +0.1 billion.

Then you just fill the immigration targets from the immigration source pop.

If the immigration source pop isn't enough by itself to fill up the +0.1 billion growths in all of the receiving worlds the remaining is taken from the most populous worlds who will thus lose pop to fill the new frontier worlds. To get a stable result for this mechanic you need some kind of "floor limit" rule, for example, "emigration can't drain pop below 50% of pop cap".

If the immigration source pop is more than the target worlds can receive then you have overpopulation which part is lost. They are assumed to end up living in slums outside your civilized system, emigrate to a different empire entirely, or starve. You should, of course, receive a morale penalty for creating such a dystopian future society so you better find new places for your people to live, you monster!

This way you get a limit to your pop expansion as populating your frontier will drain your center worlds.