Saturation is a relative term. There is almost no place that is so saturated that you can't start a profitable practice. The question is how profitable will it be and how much money will youmake. In NYC you can find a job, but that job will likely result in you making less money than you could elsewhere (and that's before even considering the fact that the cost of living is higher in NYC).
I do disagree with Mohs01 with regard to the implications of cash only dermatologists in NYC. I agree that, in general, if you have a large number of dermatologists that are cash only, it means that there is room in the market for another provider to enter. However, I think that NYC is a special case.
Many of these cash only derms cater to an extremely affluent patient population who pay cash because they think will give them access to the best doctors and best care. These people are not paying cash because they simply can't get into see a derm that takes insurance. It doesn't matter how quickly or easily they could get into see another dermatologist, they want to see the cash only ones that have an established reputation.
This sort of practice can really only flourish in certain parts of the country where there are many very wealthy people.
This situation is very different from that of cash only derms in West Texas (for example). In such areas, some physicians take cash only because their patients have no other nearby options, so there is no need for the physicians to bother themselves with the issues associated with taking insurance. If several derms that took insurance moved nearby, then the cash only derm's business would be severely affected (which I believe was Mohs 01's point).
This is in disctinction to the NYC situation where the well-established, cash only derms will have wealthy, cash paying patients no matter how many derms who take insurance move into the area.