It's not obvious that Uber is exclusively the higher-class option. Someone could easily make the same calculation you just did and decide that for them even owning a car wouldn't be worth it, they'll just do Uber every time they need to. You can afford to own a car and do Uber anyway, others can only afford to Uber occasionally when needed.
I don't have data to back it up, but I would actually be surprised if the average Uber customer in NYC owns a car at all.