Why? From what we see and hear, Cochrane is a big thing for humans. Not so much for nonhumans - the only such to express admiration is Spock in "Metamorphosis", and he's merely reciting the known facts of
human admiration of the character.
No doubt Andorians worship their warp inventor, too. Or if the story behind Andorian invention of warp was less enticing and glamorous, they might worship their inventor of phasers, or transporters, or artificial gravity. Many cultures would have those, while others would have gained access to those technologies from their interstellar neighbors, or oppressors, or victims. Humans just happen to be one of those cultures where there's a single known native inventor of warp, and apparently of transporters as well. (Although the latter might simply have been building on previous Vulcan research.)
Sounds pretty natural to me. Everybody has their heroes and villains; no need for everybody to have the same ones.
you have to decloak to fire weapons
It never made much sense that this would be the case. Of course, after you
have fired weapons, you have revealed your position (because weapons fire itself isn't invisible in the general case), and it makes limited sense to remain invisible then. But you should still be able to squeeze out the first shot unseen.
It's just that Trek weapons don't tend to kill with the first shot. Unless the target is unshielded... But that happens fairly rarely.
Timo Saloniemi