>However, when you ask your Product team to own QA, you get the real good stuff - "Why does this feature not actually work well with this other feature when you combine the configuration" etc. It's great!
This works right up until you hit a complexity point product can't handle, or worse, you find out that product is building something completely different from the requirements SME's are giving.
Your QA group (or misguided product group) can do jack squat about badly translated reqs or the right questions not being asked, which in the presence of the best devs and QA's degenerates into building the wrong thing perfectly, which has to get redone over and over again. A good QA that's been around the block is usually pretty good at sussing out major communication defects, but it can be tough to pull out of.
It's a surreal class of miscommunication to behold, and as close a death spiral as you can end up in, because everybody day in day out is working hard and getting frustrated but no one's getting closer to the end goal.