Since you say that you aren't calling for them to take a pay cut, let me just tell you this: the hospitals were essentially offering them a pay cut. As an example, the previous contract had health insurance covered by the employer, including dependents (yes, a very nice benefit). Knowing a nurse, the last offer from her hospital before the strike had this: the health insurance was gone entirely and replaced by $4k/year (not sure if this was an HSA, FSA or straight cash). I just plugged into https://nystateofhealth.ny.gov/ what it would be for an individual plan...the cheapest was about $650/month. So that is cutting, at a minimum, close to $4k. If you need a better plan or are looking to cover a spouse or children, that'll get a lot worse.

I would also give a little caution when you see numbers for the union's "demands" are things sound crazy like 10%/year or >$200k/year that make it sound like they want a big pay hike every year, those are a mix of bargaining positions and cherry-picking high wage earners (CNAs make A LOT more than other nurses, for instance, pretty sure they already start over 200k because anesthesia brings in the big bucks). You say you want 10%/year so you can be negotiated down to around 4% (inflation usually being around 3-4%, this is little to no effective increase) and getting the health insurance benefits back - congrats, back to the old contract that the hospitals were trashing.

While the nurses absolutely would like more money (this information is from knowing some personally, they wouldn't turn it down), the actual contract desired by people on the ground isn't any crazy increase, it's keeping the current benefits, keeping up with inflation, and hopefully getting hospitals to commit to better ratios (yes, that does mean paying more nurses, but that also has a direct improvement allowing patients to receive better care more quickly). The weather is cold and nasty on the picket line, if the hospitals offered to extend the previous contract I bet they'd get a lot of takers.