It think it is much, much easier to transition from slowish greens to fast ones, than it is to do the opposite.
I also believe the good players who play on very fast greens can get into some very bad habits with their putting stroke. It's especially true if they play on an old course with small, fast greens.
I moved from a course like that to one that had huge, slow greens, and it took me several seasons to understand that I had to change my approach to the putting stroke.
In doing that, I came to believe that a very good stroke will help to keep the ball on line even on slow, bumpy greens, and those with lots of Poa.
Now that I am back on a course with tiny greens, that are usually reasonable fast, I have to take care to maintain the kind of stroke that will allow me to putt effectively on other kinds of surfaces.
Ken