>> what evidence do we have that the limit is not us?

This is just such manifestly wrongheaded reasoning as to be almost laughable.

I think there's a substantially better argument against this notion than to actually try to find evidence against the claim. I prefer it because it reveals the total wrong-headedness of this style of reasoning. The argument is to turn it around and say "what evidence do we have that the limit is us?" A human level of intelligence seems like an incredibly and oddly specific level to be the maximum permissible by physics. And oddly specific claims need to be treated with extreme skepticism, because they carry high entropy, in violation of Occam's razor.

If you want to know what x equals, you don't pick a number, say, 2, assume x=2, and ask people to provide you with reasons why it shouldn't be 2. There's an infinity of numbers, and the odds are just overwhelmingly against x happening to be 2. You start with the assumption that x could be literally any of the infinity of numbers, and start looking for evidence which narrows it down.
More concretely, if you want to know the physical limit to intelligence, you start with the assumption that it could be anything, constrained by the evidence that's currently available. In this case, the evidence is that human intelligence provides a lower bound for the maximum physically allowable intelligence.

Positing that our intelligence is the maximum possible becomes even more suspect when you consider the process by which our intelligence came about - evolution.

Firstly, evolution is a process which tends towards reproductive fitness, not necessarily towards intelligence. Intelligence is selected for to the extent that it makes something more likely to reproduce, and no more, and it probably isn't the case that more smarts universally leads to more reproduction. In fact, most modern research suggests the opposite, with people with higher IQs having less sex.

Secondly, we know that natural selection gets stuck in local optima. If your species is on top of a 10 smart-points hill, and in order to get to get to the 1000 smart-points hill over there your species has to mutate in a direction that makes it stupider before it gets smarter, your species is going to stay on the 10 smart-points hill. This is because individuals that mutate stupider in the direction of the 1000-point hill will be selected against.

Thirdly, natural selection just isn't a very powerful optimization process. It works by random mutation, and it takes a lifetime to make a minuscule change which may or may not be in the right direction. Even if natural selection was solely optimizing for intelligence, and it could somehow avoid local optima, there would be no particular reason to believe that the world had existed long enough for the smartest possible organism to evolve.

Fourthly, as _greim_ touches upon, evolution has a very limited medium to work with. All it can do is change the sequence of DNA base pairs, and produce inefficient meat machines that run on respiration. There are all sorts of complex arrangements of matter which might be intelligent, and biological ones are only a tiny subset of those possible arrangements. The odds of the smartest system physically possible residing in that little biological subset are tiny to begin with, and only get smaller as you consider the more direct arguments against biological systems mentioned above, like sluggish neural transmissions, etc.