Nonstandard Rights Protection

My old friend Glen Whitman emails to offer a query for libertarians—actually, an instance of a broader question I've always found interesting. Glen points to this Mark Kleiman post citing a study which purports to show that children born to low-income single mothers are less likely to commit crimes if a nurse visits them to provide some basic childcare tips. Assume just for the sake of argument that the study gets it right, and that at some margin, more crime-per-dollar is reduced by these nurse visits than by spending on police and prisons.(I can imagine objections bearing on long-term efficacy, or concerns about what sort of advice government-hired nurses might dispense, but in order to isolate this question, let's pretend for the moment that the advice is both effective and uncontroversial and isn't otherwise being supplied.)

The question, working under those assumptions, is this: If you believe it's a legitimate function of government to protect people from crime by funding police and courts, would it be equally legitimate for the state to seek to reduce crime by this method? If not, why not?