The problem is that different places would have different levels of funding. Long Island has some very poor school districts right next to some very rich school districts. It would make more sense to have the funding not be so local. Also, property and sales taxes are rather regressive.
It is important to note that the primary reason why emergency room visits are so expensive for patients is that they have to treat everyone, even people who can't pay. Obviously a universal health care system would make that system be less crazy.
That would depend on what sort of system you wish to apply.
Btw the Irish experience has shown that a singular health bureocracy based (usually) around the main city is generally not really a very good idea (though it should pointed out that this is a relatively recent issue; Ireland was much more decentralized until recently in towards health) and this is in of course a country much smaller than many US states.
I quite like Storebought's idea actually (well the first half of it; also there needs to be some sort of cross-ward insurance for travellers, people moving, etc). But I would extremely doubt it's feasability. It must be said here that Health is not my major political issue though.
