Bloomberg’s mayoral initiatives were to end term limits so he can seek a third term as mayor, ban smoking in bars and try to ban large sodas. He is a waste of space.
Yes, he only registered and ran as a GOPer becuase as part of the Wall Street industries and with no prior working political relationships with NYC Dims, he knew he could not get the Dim’s party nomination for mayor, so he conned NYC repubs into thinking he was one of them - which was never true.
In some ways he was pragmatic, but his Liberal side often came through. I think he did make NYC government bigger than it was when he got into office.
And don’t forget he made sure those term limits went back again before he left office. That was just for him.