Given that Harry Kane is a pure striker, I'm pretty optimistic he fits perfectly into Nagelsmann's strategy.
I guess Harry Kane will fit in every team as a striker not only maybe at Bayern Munich.
But i also will see that not happend that he will be making an transfer to Munich because of the Money that Tottenham wants.
It takes a long time and it takes a lot of money if you really want something like this to happen, we know that Dortmund always have some talented players but it's not enough because there has to be someone who is really experienced there and when it's wanted the higher ups always let the player go with big sales money so I personally don't really feel that something like adopting a style will be done because they must be aware that the risk of loss is quite a lot if they intend to compete even though at this time they are often said to be rivals.
I agree that it takes some time and some big investors maybe , BAyern Munich was just lucky that they got Uli Hoeneß earlier as an investor back in the days.