Van Gaal is often overlooked there in my eyes. He implemented the core principles of Ajax/Spanish-style possession football at Bayern, even though he didn't manage to build a stable long-term construct & was a mess in many ways. But the impact of Bayern's 09/10 season on perceptions in Germany was massive back then, and Heynckes and Pep could build on the modernizations he brought to Bayern.
100% agree on this. Before Van Gaal Bayern were an absolute mess with no fixed identity on how to play, some turbulent up and down seasons with Magath, Hitzfeld and Klinsmann meant that there was no continuinty. Van Gaal was really the first person to stamp his identity successfully into the team and you can see that it worked well with some of the players in the team, while not going well with some others.
However badly it ended for Van Gaal, those couple of seasons changed the way Bayern played and moved them to adopt the modern style of possession based football that was being pioneered by Pep at the same time. Of course Heynckes improved on that by adding defensive solidity, Van Gaal's refusal to play a pure defensive midfield was the biggest reason for his downfall, and some counter-attacking speed, but the core of Bayern's style of play was still from how Van Gaal played. That continued into Pep's reign and further on.
That being said, I don't disgaree with what
@do.ob said regarding Klopp's influence on other teams. Bayern's play under Van Gaal is not easily adapted for smaller teams who lack the technical players to retain possession, but Klopp's fast paced counter-pressing football, often reliant of non-technical but hard-working players like Grosscheutz, Schmelzer, Piszceck and Kuba, was something that could be adopted as a measure against better teams. That I think was adapted more and lead to some of the crazy goals we see with the defense half-way up the pitch trying to madly press the opposition but being caught out, also some of the ugly football we see with teams chasing each other and neither being able to effectively hold possession.