Thus, even sinking 18k knowledge into income, the player is still only growing at about half the rate of the ai response
Actually, you are comparing wrong things.
You should compare the growth of your income with the growth of your ongoing expenses. And the value you get as result is the time to rebuild.
Should it increase or decrease as the game progresses? The answer actually depends. If your defences are solid and you only need to resupply your fleet, then your economy balance usually grows. If your fleet gets wiped, or your defences get severely damaged, rebuilding should take longer than it does at 1 planet.
So, in my opinion, economy should grow slower than the total cost of your assets. But faster than the total costs of like 30% of your mobile fleet.
The counter to the AIP increase is the increase in your total strength. At high difficulties, this growth can't catch up with AIP growth. However, you get a few planets free of AIP thanks to the reducers, so when the AIP finally starts growing, you have already gained quite an advantage. But after that, every planet you take increases AI's strength more than yours. We are talking about wave and reinforcement strength though. AIHW strength doesnt grow as fast, and the whole point is to reach the moment you are strong enough with as little AIP as possible.
So, we get back to step 1 in the discussion. The point of every game is to reach a certain amount of fleet strength in as little AIP as possible. Since every planet costs roughtly the same AIP, you take the ones that increase your strength the most until its finally enough to take the AIHWs. And not a single planet more, as the 20 AIP of cost outweights any advantage that you could possibly pull out of it.
More graphs time. I admit i just like graphs and post them at every opportunity.