> I sometimes suspect that the value of a QA team is inversely proportional to the quality of the dev team.

My experience has been that this is true, but not for the reason you likely intend. What I've seen is the sort of shop that invests in low tier QA/SDET types are the same sorts of shops that invest in low tier SEs who are more than happy to throw bullshit over the wall and hand off any/all grunt work to the testers. In those situations, the root cause is the corporate culture & priorities.