You're right about the African colonies. I think a lot of that was racial politics.
Britain was in the process of divesting itself of it’s colonies...it seems like it was doing it in an orderly way that the Foreign Office could handle. Kenya was pretty much at the bottom of the list due to the Kenyatta situation, Mau Mauism, etc. The new countries, although remaining part of the Commonwealth for economic reasons, wanted to emphasize their independence by calling themselves republics as opposed to dominions or establishing local monarchies.