>and NY doesn't have the budget to just pay everyone's back-rent, either.

They won't have to. Landlords already adjusted the market rate of new/future leases to account for x% added risk of eviction moritorium. NYC, and renters across the US, will be making up back-rent via higher future rent.

Of course, this is only one part of why rents have risen so sharply over the last two years.