I believe it was a committee of Okinawan masters who went about modifying karate for Japanese school kids, probably with Funakoshi at the forefront of the movement. I heard that it was primarily to strengthen and discipline the boys for military service. During the 1930s, Funakoshi's son Gigo began further modifying Shotokan in Japan by widening and lowering the stances, expanding the movements, and using higher kicks, creating the characteristics of modern Shotokan. I heard that the karate roundhouse kick came about either at this time, or later, when karate competitions began taking off. Mostly as a horizontal version of the front kick to go around blocks.
I remember reading that judo was under consideration for the Olympics as early as the 1930s(?), but I don't remember if Kano was for it or not.
As far as the U.S. occupation of Japan, apparently it was arts like judo, kendo, etc. that were mainly affected by the ban on MA practice. I heard that karate largely escaped the ban due to being seen mostly as a 'dance'. Probably due to only kata being seen by U.S. authorities in Japan. I believe the first karate shiai (competition) occurred around 1957 or so (I'm too lazy to look it up).
Also, when karate was originally introduced into Japan, there was initial reluctance among many Japanese MAists to accept karate as a 'budo'. It was seen as a 'lowly' backwater Okinawan MA suitable only for brawling. Another reason why Funakoshi modified karate from 'karate-jutsu' to 'karate-do'.