Guess I've been lucky thenI agree, but just fyi the incidents I had were actually with fairly taut bird netting. When they bounced off the netting (at an angle I guess) they grabbed at it with their feet. So we'd find them with their feet stuck through, not truly tangled, but a twist to the hole holding their foot. It wasn't hard to get them out but they weren't able to free themselves.
But you're totally right that loose bits and folds are the worst!

The last time I had to make a top for a brooder I used hardware cloth on a cardboard frame, but wire mesh wasn't so expensive back then...