Agreed! I did have some good experiences at my last job with the QA team, but it was definitely a unique model. They were really a "Customer Success" team, it was a mix of QA, sales, and customer support.
These "Customer Support" reps, when functioning as QA, knew the product better than product or eng, exactly how you're describing. I did enjoy that model, but they also did not write tests for us. They primarily executed manual test plans, after deploys, in production. They did provide more value than creating noise, but the engineering team still was QA, at least from an automated test standpoint.