No sensible club should think like this.
Although Klopp wasn't manager for the whole season, Klopp was given a new contract after finishing 8th in his first season without any trophies. The reason for this is because the club recognised the synergies between the way he managed and the way the club wanted to operate (in his first transfer window he pulled the plug on a £30m deal for Teixeira because he felt it was getting too expensive and we could spend better in the summer, he wanted the club to spend £50m on a new training ground rather than a bigger transfer budget etc etc) and that despite the inconsistent results, there was clear progress in terms of performance and developing a way of playing.
ETH's biggest problem isn't the poor results but the standard of performances and the lack of a style of play. Even when Utd have won, more often than not they've still played terribly and not only don't Utd play a front foot, positive style of football that you expect at a big side, nobody can tell you how Utd play. Even under Ole (at least until his final season) Utd had a way of playing - Utd were a counter attacking side. They'd sit back and hit sides on the break. After 2 years at the club, Utd still have no style of play under ETH. They just go out and hope for the best, typically get outplayed by whoever they're up against and rely on a Fernandes or Rashford to pop up with a goal.
If Utd are going to be run sensibly moving forwards then whoever comes will be given time if they can show that they're building towards something. If they can develop a system and way of playing and start producing better performances. Results will follow if you get those right but you'll never get consistent results without them.