Everything you just said is fantasy. You're in denial of reality, how humans behave, and the mating habits of our species. Abstinence doesn't work precisely because we're imperfect beings, ones which generally crave sexual activity on a regular basis.

What you wrote is akin to saying, "If only people would just do the right thing, all the time, then nothing would ever be wrong!" It's silly, infantile reasoning.

As for why the government should use tax-payer money on this? Because that's what governments (are supposed to) do: subsidize things which apply broadly and have a tangible, positive effect for society. There's really no downside when you consider just how little of 'your' tax money goes toward this, and how much of a net positive it provides. Like I said: lower levels of unwanted pregnancies, fewer abortions, less welfare money going toward unfit parents, etc..