The common notion appears to be that by bringing in a manager who suits your current playing style/tactical preferences, it provides greater scope for continuity and ultimately, success. I remember thinking that Pep would have been a great transition and extension on what Van Gaal was attempting to produce at us. Just taking the link posted by
@jasT1981 at face value, though with a huge pinch of salt, question becomes how similar are ten Hag and Ancelotti stylistically and who would be similar to Ancelotti if you were thinking of a long term successor for him?
They aren't really similar at all. Ten Hag has an ideology and is seemingly very set on how players should execute their roles, with little deviation possible for the system to keep fucntioning. Ancelotti is more of a man manager with a huge scope for tactical adpatability, and there are few like him. Masimilliano Allegri, Pochettino and Eddie Howe probably fit the bill the most. There are probably some young managers I'm forgetting, maybe Amorim or something. However, we've gone the Ten Hag route. The style he wants to play requires very specific types of players, which we have slowly been buying- even though most of them aren't on the level they need to be for a very good side. Either we stick to this as a core-philosophy, or we uproot and throw most of his players on the trash-heap (again), and start over. Luckily our best aquisition (Hojlund) is a complete player and should fit any tactical vision, regardless of who is manager.
If we do keep going down the Ten Hag route however, I think it's only fair we are honest about how expensive that will be. Our two best players, Rashford and Bruno, arguably aren't that well suited for the system. Among those who are suitable, very few are good enough to be long-term stars for the team. We could stick to it, and keep building a team in that image - but it will be very expensive to do so, and it won't be quick. Maybe a great DOF can find bargains to build a good side, but being in direct competition with City and Liverpool for the same type of players and talent isn't the best place to be. Perhaps it was a mistake to go down this route to begin with - but we have to make a decision, and quickly.