I do agree.

IMO the difference is that academic skills are high stake for all kids, whereas sports is only that high stakes in *some* cases.

But I am 100% sure that the same sensitivities around "bragging" will show up if you put together a bunch of parents of kids involved in the same competitive sport. Isn't the insane sports parent its own stereotype?

It might be even worse in that context, because the competition is much more explicitly set up to have a winner and (many) loser(s).