I think that's an unwarranted presumption. Even some worthless, amoral people will tend to avoid certain activities if they know an "agency with guns" may come after them for it. So I would not agree that enforcement of laws against child neglect don't act as a deterrent.
In any case, I think you have a stronger case on this issue than abortion. I would disapprove of a woman who acts irresponsibly while pregnant (heavy drinking, etc.), but I would not support prosecuting her for that as her bad treatment of her child is passive and not intentional. BUT abortion is not a passive act that may have incidental consequences for someone -- it is an intentional, active killing. If government cannot do something so basic as protecting a defenseless person against violent, unjustified aggression, then there is no point to its existence. I'm a libertarian, but not an anarchist -- the government DOES have a proper role, and it is the protection of people's inherent rights from violation by others.
Secondly (excepting rape), I would argue that people who have sex have already, by doing so, agreed to provide sustenance for whatever offspring results. They cannot selfishly change their minds once they have placed a child in a situation from which it cannot be extracted.
As for any other way to deal with, say, child neglect, I can't think of anything better than an "agency with guns" except maybe for vigilante justice, which in reality is just another form of local government, an informal "agency with guns."
Here is the problem, I think. The kind of people who would actually be guilty of the kind of child neglect government is supposed to prevent, are not prevented from that neglect by the threat of government. The kind of people who might be concerned about government interference in their lives, are not the kind of people who neglect their children in the first place.
So, the first strike against the "agency with guns" scheme is that it does not work. Want proof it does not work? How man child abuse cases did you hear of thirty years ago? (Maybe you didn't hear of any, since I do not know how old you are, but I can tell you, they were very rare.) The number of laws and agencies and personnel the government has to prevent these 'crimes' has steadily increased in those same thirty years, with a corresponding increase in abuse and neglect cases. It doesn't work!
The second, and much more important fact is, once the government has the kind of power it needs to interfere in the private family lives of individuals, it will use that power both irresponsibly and (since the agencies set up to carry out such policies must be funded) to further its own power. It will definitely end up using that power against innocent people causing more harm to families and children than would ever be caused by the individual incidents or private individuals.
Most people care a great deal about children, all children, not just their own. Not every one does, but many of us do. There is nothing in the world preventing us from taking private measures which offer "no-strings-attached" help to those kinds of people whose desparation or ignorance or just plain irresponsibility might lead them to abuse or neglect their children. If this will not work, what makes you think forcing people at the point of a gun to "help" these people will work?
Hank