This^^^^^. Having a union would be a great perk, but, at the end of the day, how many residents actually place pay, benefits or working conditions above connections, prestige and quality of training when choosing a residency?
My understanding is that if the answer was "everyone," that all the hospitals in NYC, including NYU, Columbia and Cornell, would be the easiest places in the country to get a residency, given how poorly residents are reportedly treated in NYC hospitals. Nursing unions there have a ton of power, and many over worked and under paid nurses apparently use it to treat residents like absolute crap.
In addition, the culture of medical training in NYC is just a lot more abusive toward residents than in many other parts of the country. Salaries also totally suck in relation to the cost of living there. It's just something you deal with in order to get world class training before moving on. After all, residency is not the end game, it's just the next step in training.