That has been done for years. Schools today are constantly teaching kids how to share and treat others. If not in schools then most churches in the country teach the same thing.
I think your mention of deadbeat dads is off the subject. A dad has an obligation to a child he fathered. But if someone that has no such obligation does not want to help others then how do you force him?
As a social obligation we believe should be enforced, dead-beat fathers are relevant. The more general point is that we think some obligations are so important that we do not let people opt out of them. Raising kids is one. I start there because I think we agree on that one. The question gets trickier when we ask what obligation we have to other peoples kids. And that gets us squarely to the matter of taxing some people for public schools for other people's kids. There are people who object to that. There are people who object to paying taxes for parks they do not go to. So, I think the real question for us is "do we have a clear notion of social obligation that will give us guidance for when we think nonperformance a serious enough matter to enforce performance?" I'm of a view that none of our institutions would last long if we didn't believe some obligations enforceable. Do you disagree?