You are correct, my error in skim reading too fast.
> It could just be that the theory knows its limits.
Yes that's essentially what I meant by chaos, if you could know enough information you could predict where all your hammocks end up, but that requires vast and subtle knowledge about how you think and minutiae of your environment and how you interact with it that caused you to make arbitrary decisions... the interesting thing about chaos is that it _can_ be deterministic, in other-words, given initial conditions it can be computed - but even then in the context of such large systems that computation is infeasibly and irreducibly costly, in which case (i guess) you use free parameters in combination with what conceptually similar to statistical mechanics?
Free parameters which significantly outpower the power of the observations are damning because there is no way to falsify the theory: if the theory can explain an extremely wide range of observations by tweaking the free parameters then it has much less predictive power and should be viewed extremely suspicously.
I think the trouble with dark-matter-as-WIMPs is that the free parameter (the location of those WIMPs) is overpowered:
You can say that the extra gravitation is caused by the presence of these particles and leave the details of how those particles got where they are out of your theory. But then when you add "oh, and they can't be detected by any other means" it becomes a problematic free parameter because wait a second, that's the very problem we were trying to solve in the first place. If you can't connect the causal agent to anything besides the problem that necessitated it, then it might as well be a ghost.
> Importantly, [entropic gravity] also explains (without invoking the existence of dark matter and its accompanying math featuring new free parameters that are tweaked to obtain the desired outcome) why galactic rotation curves differ from the profile expected with visible matter.
I get that entropic gravity doesn't use free parameters.
Also, I don't think that free parameters are necessarily so damning. I happen to have more hammocks than usual in my house. Any theory about how hammocks are distributed will either fail to explain the concentration, or will predict that hammocks are more likely to be found near people who like them, and then will subsequently fail to provide a way to derive the location or distribution of those people. That failure would be a free parameter. It's not necessarily an indicator of wishful thinking. It could just be that the theory knows its limits.