Their problem is that they are steeped in the past and think that they have to return to their (Ferguson-ian) roots. The problem, however, is that Ferguson had no philosophy and no identity as a way of playing. Ferguson was a great manager, but he was no Cruyff, Sacchi or Pep. He needed help from Queiroz to have success in Europe in his later years. Football has moved away from his ideas about the game, partly because of a certain bald genius.
Truth is, there's no such thing as the United way when it comes to playing football. Being fast and great at counter-attacking are things which are implemented by many teams, e.g., Liverpool. The trick is to be able to do fast transitions without losing the ball cheaply and without being all over the place when that happens. Otherwise, you are too open and vulnerable to counters. The PL has changed dramatically since Pep's arrival. Many teams are very good at possession and know better how to resist counters.