Earlier quoted context omitted.
I think you're right to bring up the NFLT, but I don't think it is applicable, it just points at the real question. The key assumption to get the NFLT is that each environment vote has the same weight, i.e. we are targeting a uniform distribution on objective functions / environments / problems / whatever you call it. If you break this assumption, you get an opposite result which is that search algorithms divide into…
Right, the environments are not uniformly distributed. In fact, the paper actually defines not one single intelligence comparator but an infinite family, parametrized by a hyperparameter which is, essentially, a choice of which environments vote and how to count their votes. Crucially, this doesn't change the truth of the structural theorems (except that some of the theorems require the hyperparameter satisfy certain…
Like I said, I only skimmed your paper, so I hope it was clear my comment was not intended as a criticism (or even as a review) :)
I think I agree with the general terms of your conclusion personally.