City Councilman Peter Vallone Jr. wants to hold fathers responsible for their children’s well-being.

That may sound like a no-brainer, but alas society — particularly in New York — has let too many dads off the hook too easily, and for too long.

At the children’s expense — and the taxpayers’.

That needs to end. And Vallone’s got a reasonable plan, which he outlined on these pages yesterday, to help end it.

In a nutshell, Vallone intends to introduce a resolution in the council urging the state to require a father’s name on a child’s birth certificate before a mother is eligible for public benefits.

That info can help the state track down these men and bring them back into the family’s financial picture — and, perhaps, into the lives of the kids themselves.

And it can save the state a bundle, too — an increasingly vital goal as both the city and state face ever-more-dire fiscal challenges.

Start with the fact that, as Vallone notes, “more than $5 billion in child support has gone uncollected” in New York.

Vallone says unmarried fathers “can get away with not including their names on birth certificates — making it easier to stay completely out of their children’s lives, especially financially. A mother is also eligible for state child-care benefits without ever acknowledging a father.”

That’s insane.

Let’s face it: Despite New York’s outrageous, nation-leading tax burden, government still doesn’t have enough money to let parents, fathers or mothers, shirk their responsibilities to their kids.

Fathers, in particular, can’t be allowed to remain anonymous so as to avoid paying their share.

Think of Vallone’s plan as the next step in welfare reform.

Indeed, his measure — which he intends to introduce on Dec. 20 — is modeled on recent steps in Britain (where the government faces a critical budget crunch) meant to curb welfare outlays and promote paternal responsibility.

Even more important than the measure’s financial impact is what it can do for kids. As President Obama himself observed two years ago: “Children who grow up without a father are five times more likely to live in poverty and commit crime, nine times more likely to drop out of schools and 20 times more likely to end up in prison.

“They are more likely to have behavioral problems or run away from home, or become teenage parents themselves. And the foundations of our community are weaker because of it.”

Knowing a father’s identity gives public authorities leverage over his role in his children’s lives — even beyond forcing him to write out checks.

That would be good news for kids.

And knowing that a dad’s name must be cited for a mom to get benefits might even deter some pregnancies by parents who’d otherwise expect taxpayers to foot the tab — and by fathers who have no intention of hanging around.

Vallone’s plan is essential, financially and morally. Let’s hope New York’s pols are listening.