There's a basic loop that goes on regardless:

1. define a requirement 2. implement the requirement 3. verify that the requirement was implemented

TDD was built around the idea that 1 and 3 could be unified in automated testing, and that's certainly true for a large part of it. But QA as a discrete role needs to exist because, beyond verifying that 2 was done correctly, they expose higher level bugs in 1, the requirements themselves.

It's virtually impossible to define requirements completely and without second order interactions that cause problems. QA is as effective at exposing assumptions and handwaving by the people who created the wireframes or the visual design as by the developers failing to test their own work.

And ideally, this leads to the cycle being virtuous: higher quality starts at the requirements phase, not the implentation phase. It's not just that QA should work closely with the engineers--the engineers need to work closely with UX and VD to ensure they fully understand the requirements. The incentives are aligned among all parties.