Not many big level managers actually end up changing their style of playing for the team they are on. Look at the games Mourinho played in real Madrid and look at Chelsea and now look at Spurs, they are all different from each other.
I mean even Pep is playing a style he is close to and maybe its not the same as Barcelona but it surely does resemble Bayern for sure, his time there was short lived but he played about the same game he is playing now and he is still a great coach. Sir Alex Ferguson, who arguably could be the best Manager ever in history of premier league played the same game for 20 years, with all those players changing, his system was amazing which nobody ever said anything and he kept being successful, but changing your system depending on the players you have is a rare talent for sure.
That is why there should be a coach, who may have his tactics, but he must adapt with his team.
Sir Alex Ferguson had an idea strategy that was incredible, and every MU goal was brilliantly tactical, making it the best coach of all time in my opinion.
And in order to use his tactics more easily, he had a very good sense of choice, he had a great analysis for each player, at least for a brief look at his game.
He is not from this planet.