I don't think this is really true. Woodward and the board have been plenty willing to spend lots and lots of money on players the manager has wanted. The bigger issues are that (a) Woodward has no meaningful football knowledge whatsoever and seems uninterested in hiring DoF, so that level of the club cannot provide a true footballing direction and therefore (b) you need to basically concentrate the football decision making with a strong manager with a good grasp on current trends in the game and a very strong sense of the football he wants to play and the qualities players will need to play that football at each position.
I'm not sure that Allegri is the answer but I am pretty sure Ole isn't either.
Your point b) is very true but who are those managers apart from Pep and Klopp?
Almost anyone else is a gamble. So we can only get rid off Ole if he has a bad season, if we are not making any progress or if such a b) type manager becomes available and wants to join United under the current board structure.
Even someone like Poch has a system with no plan b AND once his team peaked everything was gone the following season: system, performances, results.
