I understand the argument you are making but our country isn't set up that way and will never be. So since what you are arguing will never happen the best way to lower costs, if that is your goal, is to reduce poor people from having kids. How are ways we can do that? Have them abort them if that is their desire or do everything we can to help them not get pregnant.
At one time, not to long ago, it was set up that way so it can be that way.
If you aren't going to support people being required to support the kids they have, that only leaves one option and it involves ways to keep them from getting pregnant. If you continue to have kids you can't support, there are operations that can prevent pregnancy. If people are going to be human then demand others foot the bill, I have no problem with making it where they can't have any more.