Yes. That is what I've been saying all along -- the research penalty is too harsh and should be scaled back.
My position on AW and expansion penalties is that they would be okay once the research penalty is scaled back.
In particular, if you are advancing (and that is an 'if'), then you can choose AWs and expansions such that they help more than they hinder.
If you are not advancing, they help even less, so there is a motivation to keep them down, though the very best AWs do still pay for themselves. (Yes, I am cherry-picking, but since you get to choose which AWs to build, I consider that fair.)
In other words, I believe the scaling is about right for AWs and expansions, but the extra multiplicative factor for research makes the costs too large.
You really haven't worked out the math on that one because what you are saying isn't true. The squad size increases massively from AW levels and expansion.
All things equal, I calculated a 35% increase in squad size from being at the end of chapter 16/beginning of chapter 17 and the end of chapter 18, so 2 full chapters.
The range for AW is a 355% increase from zero to all, and the range for expansions is from say all placed free expansion and that plus all premium expansions is 30%. Combined those make up about a 500% increase in squad size. It is definitely highly regressive and I estimate it is 2 to 3 times higher than what the benefits can make up for.
Military speed for all three of the military buildings increases by a mere 17% where squad size is increasing by 35% from the two chapters, and it would have been about 29% if chapter 18 didn't have such a huge number of extra tech. So there is a net decline from the tech tree, and relatively speaking the squad size increase was double the increase in production capacity.
But maximum increase in military speed from any AW on troop production is 46%. You get 46% increase in troop size with 153 AW levels, but you need 105 AW levels to give you that 46% increase in military speed. There are AW that make you stronger and and improve your health and thus slow down the rate of loss, but they cap at 40% stronger. Those increases come with increased goods costs for negotiating, with that increase in squad size you need 46% more in manufacturers to keep up with the cost of negotiating with goods, which requires more land, which will further increase the squad size resulting in needing even more land for manufacturers to keep up.
I made a suggestion that the AW piece in the equation might be ok if they took the square root, so the AW part of MinMax's formula (0.003A +1) would give a max 113% increase in squad size from AW, and with maximum expansion would be about 150%, so if squad size is 800 without premium expansion or AW levels, it would be 2000 with max AW and expansions.
So what they came up with they were happy with and (0.006A+1)^0.5 for A=1 give the same hit to start, but would put the maximum range from AW to 185%, which combined with the premium expansion would be 240% increase, so that maximum squad size comparison would be 2720.
Right now when I use the formula a chapter 18 player with just the free expansion and no AW would have a squad size of 612 for the tournament, and then the maximum squad size with premium expansions is 3614. The first square root suggestion would make that squad size range 612 to 1530 and the second 612 to 2080.
I think the problem with the technology hit is that improvements we were given didn't match the tech hit and I think that's where that should be corrected.