The New York accent has become inextricably linked to the working class. If you have middle or upper middle class aspirations, you get rid of it very quickly. It's different in other places. For example there are still upper class accents in New England and the South (like Jimmy Carter or Ted Kennedy). It's very rare to hear a professional in Manhattan with a New York accent, at least one that's very pronounced.
There is an upper class New York/Long Island accent (like George Plimpton) but it's very rare nowadays.