Yes, that is exactly what I'm saying (again, with the understanding that there are accidents, people who get laid off from better jobs, etc.)

And I am advocating for fewer people being born into poverty.

Why are you opposed to this?

Your method is that poor people should not have kids due to their inability to easily provide for those kids. In not having kids, they bring less people into an impoverished social standing that is hard to break out of. By this reasoning, should people with less desirable traits (history of heart disease, cancer, etc) not have kids to help eradicate those traits? There is a chance their child will not have those specific traits or htey will take, like there is a chance that a child will move out of poverty.

Of course not, that's absurd.

Other than the self regulation of impoverished people to not have kids to help eradicate poverty, which is what you are describing, I would rather see social means to help those people escape poverty.