If only certain people are encouraged to have children, you automatically have an underclass, no matter how it's implemented. I think that providing free (or more incentivized) birth control would lead to very few cases of unwanted children. IUDs and vasectomies are simple and effective.
> I think that providing free (or more incentivized) birth control would lead to very few cases of unwanted children.
You'd be surprised
I don't have data at hand, so I can't contradict you with evidence, but you could also provide some numbers with your claims. I know of Project Prevention [1], which pays drug addicts for long-term birth control. The Wikipedia article doesn't provide data on effectiveness, but I guess they'd stop handing out money if it didn't work.
This will only mean the most vulnerable (who need the most support) will be unsupported. You're creating an underclass.