Pictures in the 1940s and 1950s shows these guys mostly insuits often with fedora type hats
Even earlier
And yes,they probably wanted to fit it with the businessmen and politicians and other upper crust people rather that rely on committing street crimes
Back then if they were together at a crap game or social club,they probably dressed more casually but not in ripped jeans an a T-Shirt or a baseball cap turned backward
Somehow they managed to dress well and still not get exposed as being part of a criminal society for many years
I think rich people including politicians these days often are associating with people dressed like bums as long as they have some kind of reputation or fame or wealth and can influence large followings.
I think that one of the biggest components figuring into the way so-called 'wiseguys' dress today has mostly to do with the era they find themselves in. They're dressing habits only mirror the larger population and the mindset in America today.
The average businessman, unless he is on Wall Street or operates from Park Avenue as a lawyer or top corporate official, generally does not dress in a business suit or even in dress slacks and a button down shirt. Say what you like about that, but it's just not the way it is anymore.
The average man or woman dresses much more casual today -- even when they go out to dinner in a nice restaurant. How many people in the finest of restaurants even wear a sports jacket nowadays? Not many! 90% of the finest restaurants in NYC don't even require a 'jacket' anymore.
....sign of the times.