To be fair, I don't think that making a good impression with the City fan base was at the top of his agenda!
As a Chelsea fan I did research Boehly and other potential buyers during the bidding process. My feeling was (and is) that he was the best choice, all things considered. He wants to win as a priority, and the financial backing demonstrated so far, albeit chaotically, supports that.
And as far as being arrogant, I just don't see that but it's subjective I guess.
I'd like to think that sensible Chelsea fans will realise that what happened to our club as a result of Putin is going to take quite a while to work through. And in the mean time fans of rival clubs can enjoy watching one of the strongest prem teams of the last twenty years go through the pain. I would :)