NYC generally doesn’t have this stigma as bad as the rest of the USA. Wealthy people and celebrities ride the MTA.
Celebrities, politicians, billionaires all ride the subway all the time. New Yorkers know to keep to themselves out of politeness not safety and honestly are more likely to step up and defend someone famous being harassed than join in. We're all just trying to get to where we're going and the subway is almost always the fastest and most convenient way (not to mention cheapest) to do that.
According to you? Riding subway in NYC and you'd see plenty of rich people. Go to any station near the financial district, or Park Ave.