"Should" is one of those words. QA absolutely should not exist. Developers should not write buggy code to begin with! But they do, so QA (in some form) must exist for software to be any good.
It's not just finding bugs, QA people are the people who actually USE the product, every part of it, every single day. They find pain points and things to improve and things that don't make sense constantly. But yes they're also really good at finding bugs.
