Why the desire for low magic?

[Batcathat]

I find it very unrealistic that every challenge a DM prepares for the party needs to be politically correct and be somehow solvable by every player of the table. Different players will have the spotlight in different encounters.

I agree with the sentiment that not everyone has to be able to contribute equally in every situation, but the problem is that in D&D some classes can contribute in a whole lot more situations than others. A GM can create situations where the wizard can't contribute for some specific reason (such as the "must defeat the champion barehanded" example you give) but using that alone to make sure everyone contributes a roughly equal amount would probably feel quite contrived and railroady.

it should be a matter of table etiquette that the magic dude don't upstage the martial dude on a martial-themed challenge by summoning a beatstick

A system where some characters have to intentionally limit themselves in order to not always outshine other characters is not a very good system, I think.