I don't think anybody is saying that proofs don't matter, or that they aren't important. But it looks like you're choosing to focus on uncommon edge cases. I think a lot of people would question that line of thinking. It's almost like the old saw about how you don't need a degree in mechanical engineering in order to effectively use a car. But if you need something "almost like a car, but also kinda like a bulldozer" then you're out of luck. OK, how often does that scenario come up? Enough to care about? For most people, the answer is a resounding "no".

Likewise, one can certainly apply a lot of mathematical techniques in a lot of situations, without proving new theorems. So there are edge cases... not the end of the world. Deal with it when it comes up.