Absolutely QA "should" exist. Our QAs are the most knowledgeable people on our product, often informing devs and product alike of requirements, missing requirements, weird configuration outliers, how to actually use the damned app, etc. Without QA we would be developing and testing for brittle requirements to get code into an MVP state, not a functional, user-friendly state.
"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.