While I agree that football is a results business I definitely don't expect to get good results from a poor squad and I don't want the manager to get the sack if he doesn't achieve his ambitions. But what I've seen happen in every club is exactly that, except for the very rich ones where the managers get excess credit for the best players playing well.It depends on who is appointed. A club like Brighton has a clearly defined philosophy and style of play, with clear parameters defining their market strategy and this philosophy informs who they approach in the first place, which is why they can transition pretty seamlessly from one manager to the next.
I think we are living proof to the fact that it can often be an enormous tweak and that is if the club willingly opens the door to a radically different philosophy. The shift from Poch to Mourinho was disastrous and currently the shift from Conte to Ange has been extremely difficult and is yet to show any sort of consistent improvement.
United have had a similar experience, lurching from SAF to Moyes to LVG to Mourinho to Solksjaer to Ten Hag...all of them have very different interpretations of how the game should be played.
So I think you are fundamentally mistaken. The philosophy comes from the Club, not the manager. His role at interview is to demonstrate how he aligns with that philosophy and how he will implement it in reality to improve results. Because ultimately this is a results business wherein unlike other businesses which can and will absorb multiple terrible years running at a loss before hitting a growth stage, football moves far too quickly and under far too much scrutiny for that, so ultimately results are more important than philosophy.
The problem we've had imo is that Levy and the DoF haven't provided a unified coherent philosophy from the top down, while simultaneously not empowering managers to at least achieve results in their own way. Our treatment of Jose and Conte was akin to giving Lewis Hamilton a Fiat Punto with an iffy transmission and sacking him when he doesn't win the grand prix with it.
I don't think we can say that any of our managers have over or under achieved. None of them has really departed from where we would expect to finish allowing for scatter and uncertainty. Even Poch's success could be attributed to accidentally inheriting a squad which was much better than the price we paid for it. He certainly hasn't done anything since leaving us that shows he has any special coaching talents.
If you remember Mourinho specifically said that he was very keen to work with the group of players we had. I reckon he basically told Levy that Poch had underachieved and he could do better. Hardly surprising that he didn't last long when he didn't achieve anything.
I think Levy has generally tried to get managers with an attacking philosophy, the exceptions being Mourinho (for the reasons stated above, I think Levy was seduced into hiring him) and Nuno/Conte which Levy clearly delegated to Paratici. I think sacking Jol and Poch early and those three hires were big mistakes.