But for the same population, you could separate your populations more or less equally between a number of colonies.
So instead of 1.5 billion capital + 5 other 25 million colonies, you have 2x 700 million pop planets, 4x 25 million colonies, and that'll grow population faster than the single big planet version.
And the fastest population growth is when you divide all 1.5 billion into 6 equal portions. But concentration of production power must take precedence so that's pretty infeasible.
For example, in my game, I shifted all my research facilities onto another planet that had no resources. Terraformed it and moved colonists over to it.
In a period of 2 years, my capital planet population dropped by 40%, all of which went to manning the labs on the other planet.
Starting from a 1 billion pop start, I now have 1.7 billion population in 12 years. Not sure how much that is but linearly, that's a 5.8% growth rate. Of course, actual growth rate is probably closer to 4% or so but that's loads better than if I had kept everything on one planet.
My aim is to grow them both to 1 billion pop, then set both to source and move colonists + automines to another system in order to have two major industrial centers. At this time, my "empire" is mostly a 1 system nation with a bunch of external holdings. Can't wait to graduate to a "true" interstellar empire.