I agree with all that.
I hate it when teams unexpectedly come up , their manager has done a great job getting them there but they are clearly uncompetitive and they think the answer is to sack the manager.
That said it is so difficult to arrest a negative slide and reoccurring defeats even after relegation.
So yes if I were Luton or Sheff U I'd stick with the manager.
I can't get my head around Burnley. They looked fantastic in The Championship, far too good and I thought they and Kompany would stay up comfortably. However they have been rank and now lost their only striker for god knows how long.
I genuinely don't know what I'd do if I was Burnley's owner , probably stick with him I think.
Bournemouth is a really strange one. They had manager who did really well last season but got rid. Some good players there but terrible results until recently. I think you'd have to stick with him for now at least