I'm not conflating anything, I'm just refusing to along with your unsupported premise that there are plenty of loving homes to take in all neglected children.
The only possible answer is it depends. If you can pop them all into families that are dying to take them (ideally at no cost to the state), sure, "pick them up." (That sounds like you're talking about the pound btw).
If you're taking them from one sub-optimal environment and putting them in another (i.e., reality), you weigh the resources you have and see if their home lives can be improved. (Possibly by providing contraception.)
Well, you've moved the bar a little. You've already said you're not against abortion on principle, so now we're talking about rational public policy.
It depends on whether I'm screwing them.
But seriously, in general, yes. If in the anti-obesity case something costs $10 a year and drastically curtails heart disease and diabetes, why wouldn't I want it to be publicly funded? If sexy old men make society better for a nickel a day, why not?
I suggest having policy-makers look at cost-benefit data and find ways to help people in a bind without killing their incentive to do anything for themselves, while improving society as a whole.