Those three managers weren't successful because they were given time. They were given time because they were successful (or at least showing signs of it in Arteta's case). If INEOS think that ETH is showing signs of being successful behind the scenes, that is the only way we should even be thinking of keeping him. If he isn't showing signs of building something good behind the scenes, then he shouldn't be kept because he certainly isn't showing it on the field.
Fulltime managers since 2013:
Man Utd: 5 managers
Bayern Munich: 7 managers (going to be 8 next season)
Real Madrid: 7 managers (two of them having two periods in charge, so 5 different people but 7 managerial changes)
Barcelona: 6 managers (going to be 7 next season)
Chelsea: 8 managers (going to be 9 next season)
Inter Milan: 7 managers
AC Milan: 8 managers
Dortmund: 7 managers
It's basically just City, Liverpool, Atletico (all of whom had the best manager they possibly could get), Juventus (who probably couldn't get better than Allegri either) and Arsenal (who still had Wenger for five of those years) who have kept managers longer than we have.
So this idea that we're trigger happy with managers really couldn't be further from the truth. Other than maybe Arsenal, we've given managers more time to prove themselves than any other top club in the world would.