You still need a competent developer for the prompting, planning, etc. But once it's running, I want to avoid mental context switches and just have it run

Giving it access to a cheap human who is just there to take screenshots, do QA, give UX feedback sounds like a good idea in principle. It's non-trivial to set up, but I wouldn't be surprised if some companies this becomes a thing. The return of the QA department, just that they now get to do the agent's bidding in addition to checking if the results work