EDITED:
In my free time, I started to wonder if 3 is better than 2.5, and it seems that way. I didn't put much thought into 2.5 at the time. It seemed odd, but this made me think about the 0.5 part, and I have my doubts about that too, because what it means is that the maximum value going into the power function is 1, or not even, since the textures don't really go that far...
So if this is correct (it looks very correct, not just visually but the pixel values are virtually identical) then it means that this function is only marking dark values darker. I guess that's the case, and a gamma ramp typically is like a ramp instead of a bulge. Even though gamma is meant to pull out mid-range colors. I think it's that way because the sRGB color space is already itself nonlinear. I'm still bugged by the broken sword. It seems to suggest that the upturned lights are aimed further up at the ceiling, and the sword's texture is much brighter. The ceilings max out, so that no matter how bright the light on them, they can't get any brighter.
I wonder if either 1) bright colors should be exponentially brighter, or 2) if those lights need to be super bright, so that the contribution to the walls is just because the lights are not really aimed at them. But I don't think 2 is possible, because in the waterfall caves, the ceiling is darker on one side than the other, meaning that one upturned light cannot be fully white.
What amazes/annoys me is there are so many factors, that when you include the ability to adjust the lights/ambient level of light, to compensate for the color transformation function, there are many combinations that are very "close, but no cigar." On the bright side, 3 instead of 2.5 I believe does genuinely look better. I find that I keep returning to the lighting values I shared in image form a while back. I think there is some kind of ground truth to them. I feel like when they work well, it's a good indication a color function is more correct.
There are many touchstones for calibrating these things. I don't know if it would be interesting to write down the process. I may do it just to be a reminder to myself. I'm probably worked on the problem (trial and error) for at least 8 hours, if not twice that, all told.
EDITED: FWIW 2.9 looks pixel perfect... but it's not a round number. Maybe tweaking the lighting could get the same results out of 3. It's tricky though since the ambient level isn't multiplicative, and lights are point in different directions. Once you get down to very slight differences it's impossible to say if the light set up isn't slightly off.