"Absolve Verizon of customer service responsibilities"?
Why would Verizon take that deal? As far as they're concerned, they already aren't particularly responsible for customer service. But they can rake in the fees from their captive customer base.
What NY seems to be asking Verizon is "Pretty please, lay in the last mile of fiber and then step away."
You'll have to seriously sweeten the pot (such as extortionate wholesale service fees) to make it more profitable for Verizon to do this, vice continuing to squeeze its current copper-service victims for sunk-cost mostly-profit revenues. And for companies like Verizon, "less profit" is a non-starter.