It's important not to confuse understanding a topic with having been taught the topic. If someone understands dimensional analysis, sure, they won't make the mistake. But it's easy to imagine students who were taught dimensional analysis making these kinds of mistakes.

I think it's a mistake to argue that because students don't understand method X to solve a problem, they should be taught method Y. The problem is the lack of understanding, not the method.

But dimensional analysis is just another mathematical process turned into a rote method which does not require deeper understanding. The problem is not the pile of rote techniques is too small, but that students aren't learning how to actually think mathematically.

I find this "think mathematically" concept you invoke to be a bit fuzzy. Even geniuses (not me, but I've met some) can be caught out by novel constructions if they haven't had time to consider them carefully. Much mathematical sophistication consists of adding to "the pile of techniques". If a student has too shallow a pile, the goal of educators should be to pile on more. If we suspect the research under discussion represents something real and not simply a series of methodology blunders, then it points to an improvement that educators could make. It's likely that basic dimensional analysis is not a complete answer, but I suspect that an admonition to "think mathematically" is not even wrong.

> I suspect that an admonition to "think mathematically" is not even wrong.

I am not suggesting that we admonish students to think mathematically. I'm suggesting that we teach them to.