I personally don't like him as a coach. The tactical aspect he does not work well or gives it less importance than other coaches.
I like Xabi Alonso's proposal, his way of understanding football.
The problem is that Real Madrid players are more adapted to another type of football.
Valverde, Camavinga in midfield and Mbappe, Vinicius are more counterattacking players.
What I want for Madrid is someone adapted to modern football but who knows where he is coming , that is, who is willing to listen to "recommendations", or more elegantly, who works in coordination with the board, but with clear ideas.
Ancelotti is good-natured, much loved by the fans, with a character suitable for the locker room but without ideas.
The typical coach who makes the changes that are shouted at him from the stands, more out of fear of losing his position than out of conviction.
First he corrected himself with Valverde, lately Camavinga and perhaps in a couple of weeks he will decide to call someone from Castilla.
That is why I would automatically rule out coaches with a lot of character and personality and with too many tactical ideas (if I were a fan of Valencia, Sevilla, etc, surely yes).
What you say about the counterattack... I think that rather what Madrid is looking for is an intense, physical and vertical game, without necessarily being a counterattack and I think that those players could adapt.
I think that Valverde in particular has the conditions to delay his position and not Stereotype himself into a player who only runs .
About Xabi, here he talks about high pressure (you are Spanish?), which seems like it would also be a pillar in his style