You mean "screening out" people who suffer from genetic diseases. Why not "screen out" people when they develop chronic conditions later in life, too? Or any other group the rest of society may deem unworthy, like Jews, gypsies, Jehovah's Witnesses, and communists?
And yes, screening for people who suffer from genetic diseases. A lot of which we can't cure right now. But we are working on some of them. Childhood diseases are very tricky though, because they're typically quite rare, and many of the treatments are experimental.
As for screening out people who develop chronic conditions in life, we already do that. Cancer is a genetic disease that happens later in life, and sometimes we can't cure it. Sometimes that person wants assisted suicide rather than going through the pain of living. That's their choice I think.
I think the big thing is as technology progresses, and we can both cure more and people can't pay for it without insurance, what do we do? Should we cure 100 babies in Africa or one in the US? They're both life, but very different cost. Shouldn't we save more babies if we can? Does where a baby gets born imply how much we should care about it?
When you go as far as basically the holocaust, I think that's pretty crazy. We're talking about naturally occurring diseases and problems that we may or may not be able to cure. How much of someone else's money should be spent on it is an open and tricky question, as the patient would likely spend any amount to stay alive. At that point, maybe compassion is looking at the larger picture: we're all going to die at some point. But medicine these days is about delaying the inevitable at huge cost to someone else.
Really, I think the long term solution is taking the profit motive out of healthcare. If helping people live better lives isn't good enough, then maybe medicine isn't your field. And we should make healthcare non-profit and not tax it, and do other things to encourage it.
That's not a necessary qualification. For example, 90%+ of fetuses diagnosed with Down's syndrome are aborted, even though Down's is far from a death sentence: https://www.youtube.com/watch?v=Ju-q4OnBtNU
Giving a child a life like that feels cruel and heartless to me.