It would look bad on my resume. And given how much of a mess it is, it sounds like a terribly stressful job. I think any dev who doesn't see those red flags (or care about them) is very, very likely incompetent.

Honestly, even they weren't it's like a self fulfilling prophecy. It's fairly incompetent to take a job that people believe is for incompetent people. Unless you totally turn shit around, which obviously nobody has.