Thing is there is different type of coaches who sink with his ship (philosophy). He knows full well, the situation, but he chooses to pursuit his way: perfect his play & dominate other teams than change the philosophy. Just like how LVG claimed his team playing attacking football while we barely registered couple shot on target all game.
It's football; there is no absolute right or wrong. With the right conditions; we all saw how dominating his Barcelona team was. We know there is possibility for the philosophy to work. This guy believes he can replicate it; so let wait & see how it turns out. It maybe his eventual downfall or he can make it work in the end, time will tell.
I never wish him luck as City coach; and most of the time I would say he is very one dimensional in his coaching style; but I acknowledge that different people have different workable (not disastrous) views. I am only disagreeing with you on the part that: he doesn't realize the issue nor he didn't try to tweak; and football coach should do things the same way.
Edit: I defended LVG when people said he was clueless, too. I acknowledged his philosophy doesn't fit our club & he is trying to change our identity by his philosophy. His sacking is after the result is justified. I questioned people who saw Pep as good United coach when there was some wild link by the papers, by explaining that if you feel well with purist in LVG, you wouldn't with Pep. They are different but are same as purist.