What you elaborating on isnt a valid basis for the first statement you made. Style is just part of the equation. Some clubs have specific styles and identities but ultimately it's about better and more successful football that leads to winning. Especially CL that requires that extra gear.
All the clubs you mentioned fired their coaches for better results or require higher standards, only exception is Arsenal with Arteta (or Arsenalin the past, so unambitious that they deluded their fans you value style over substance). But even there Emery was so bad that they felt forced to take a chance on an unproven former player, gambling on Pep rubbing off on him and improve their station. Or want their own version of Zizou, Conte etc.
But all those top clubs require more winning football. It happens that most of the winning teams are the best attacking teams, so it goes hand in hand, but that does not make your statement of no fanbase of big club value winning anymore. If anything, it's the reverse, coaches have so little patience given exactly because the pressure to win it all is high in absolute biggiest clubs.
And get over it, Allegri took us as far as he could, he ran out of ideas and shouldnt stay further. The fact that they might he botching up the replacement is a completely different matter.