It starts to approach eugenics pretty quickly, which we as a society have pretty much rejected.
But we do regulate the raising of children, to a certain extent. For example, we regulate school curriculum to install a certain set of values and knowledge in children. As a society, we also attempt to regulate certain kinds of parenting, by making certain forms of child abuse and neglect illegal.
I was curious what you were trying to say. I assumed you meant that Down's Syndrome is down due to testing and abortion. But I found this:
The vast majority of screen-positive results are false, yet encourage invasive diagnostic procedures that pose additional risks to unborn babies. As a direct consequence many babies who do not have Down syndrome are lost. We estimate that current screening practice in England and Wales reduces annual live births of babies with Down syndrome by around 660 and leads to the losses of 400 babies without Down syndrome. Although prenatal diagnoses are becoming more frequent, more babies with Down syndrome are being born (up 25% over 15 years).
Because it is a violation of very basic Human Rights? Not to mention the can of worms that will open. Who gets to decide who's worthy of procreation? Based on political, social, economic values? This is like codifying systemic discrimination into fundamental human rights.
One of my friends was homeless as a child. He is now deaf because of an ear infection that was left untreated. Bringing children into a world when food and safety can't be provided is a violation of human rights as well.
Yes, Child Protective Services should have prevented this from happening to my friend. It didn't.
If parents can't prove they have the means to raise a child, CPS proactively taking custody away from the parent doesn't seem that unreasonable to me.
I would turn this idea around: instead of barring certain people from reproducing (which has obvious issues), a society could require that all new parents take a course, go through counseling, or something like that, after which if they're deemed unfit to provide a healthy and safe environment the newborn would have to be adopted. This assumes it can be done to no economic cost to the new parents. It also assumes there are uncontroversial ways to determine fitness to parent. Basically a similar system to what most countries have in place for dealing with children in distress, but proactive rather than reactive. I'm sure there are issues with this idea as well, and the pragmatic way of trying to educate prospective parents is probably the best we can do, but it seems worth exploring.