FWIW I found it much easier to get a reservation at Crown Shy last minute compared to most nice restaurants in NYC, starred or not. Didn't even realize it was starred until after (probably a good thing so I don't set expectations too high).
Yes. There are 23+k restaurants, how many of those are "fine-dining"? Put another way, you could go to a different Michelin starred restaurant every week in NYC and still not go through the list...
Also, not all Michelin restaurants are that good... (In NYC, I think they are because it is so competitive but I've been disappointed in SF and Hong Kong for instance).
So FYI - just because a restaurant has a Michelin star, it doesn't mean it is always packed nor good.