Well, that's the other side of the coin, of organizational stability beyond the managers position, of course.
If you sack a manager because you feel he doesn't do a good enough job to manage the team, it follows that you will require the manager you hire to do a better job WITH THAT TEAM.
The notion that every manager gets to 'build their own team' is absurd in that context, for the reasons that you express in your post.
Any new manager after Solskjaer, whenever that transition happens, be it Conte, Ten Haag, Potter, or someone else in the future, should be able to work with the team that is there, plus a few normal, gradual additions as clubs do every summer. You have a good squad, Conte can be successful with that squad no problem.