Ok your post was fairly hard to understand, but i will explain it more carefully.
Pop bankers have the most porfitable growth of all bankers when doing it correctly, however because of the dependency on actually having population on planets, a pop bankers can only really grow at a certain speed without damaging his profitability
Many pop bankers will try to force growth to go quicker than what is optimal, (they might not like to aid out, or just plan stupid (who knows)), by spending too much cash too early on early exploration, or going to bizarre TO/LQ rations (above 60%+ TOs) because they dont have pop
Therefore i would advise poppers to have patience, the growth of population is exponential, because you are not on top of your fam early doesnt mean you are doing something wrong. You can always get passed planets later and when your planets have decent and even population you can make huge jumps towards incomes that a CF banker can never achieve.
If we assume the following market prices
Iron 11
Food 11
Endu 20
The cost of a CF is 250 with an income of 8 giving a repayment in 31 ticks (after the 5 ticks build time)
The cost of 1 building in a 50/50 mix of LQ/TO is 440 with an income of 21,67 and food cost of 3,5 totalling on 18,17 giving a repayment in 24 ticks (after the 12 ticks average build time)
The per tick return on investment is 8/250 = 3,2% for the CF banker and 18,17/440 = 4,1% for the popper
Proving that if managed optimally a pop banker is more profitable than the CF banker right from the start of the round, the issue is just to not make bad decisions as a pop banker, and dont overspend to force your early growth.
Later in the round when you add science and overbuild into the equation, the income will go even mor ein favour of the popper, but ofcourse this is allready common knowledge