NYC already has plenty of taxis. I would expect Uber to only really be used there either as a) a luxury black car service, or b) a convenient taxi dispatch service. It sounds like you're talking about them as if they're purely the latter. Surely they're acting as both? They could also be c) a cheaper alternative to cabs (as UberX), which is what UberX actually is here in SF, but I don't know if UberX exists everywhere or operates the same way everywhere (laws regarding car services are likely to not be that different everywhere, but UberX exists in a much more grey area that I can very much believe doesn't work everywhere; plus, it doesn't make as much sense when there's already enough taxis to go around).
As a luxury black car service, everything I've already said stands.
Ax a taxi dispatch service, I wouldn't expect really anything I know about Uber to apply. But I wouldn't expect surge pricing to apply either, because when Uber acts as a taxi dispatch service, you're still just paying the regular taxi fare (with the caveat that Uber guarantees a 20% (I think) tip instead of leaving it up to the passenger). And if surge pricing doesn't apply, then neither does the claim that drivers cancel when surge pricing is going up.
As far as I'm aware, the main reason for a taxi to cancel is because of laws requiring that taxis can't say no to a street fare, even if they're being dispatched to pick up someone else. This is the same reason why it can take a while to get a taxi to show up when calling the dispatcher directly, and using Uber to request a pickup shouldn't alter that at all. Of course, I could be misinformed about how that law works, but that's my understanding of it. (And of course the taxi driver could have other personal reasons for canceling, but surge pricing isn't one of them).
On this note, the $4 for canceling fee actually makes some sense, if we assume Uber was unable to successfully recruit enough cab drivers with the model of Uber being paid a flat fee for each ride. Uber still benefits by having taxi dispatch services in its app, because that means it becomes the one-stop app for people who need car-based transportation, and once you have them in the app you might convince them to go with the real Uber services. And the $4 cancellation penalty encourages drivers to not cancel, which in the absence of a rating system (which I don't believe Uber has for taxis, nor could it really enforce due to e.g. taxis being driven by someone other than the owner) is the only real way to incentivize drivers to not cancel.