My son's birth-mother did just that, in Russia. He was delivered at home, brought immediately to a hospital as he was 4-6 weeks premature, and she never saw him again.
I’d rather read about this than about an obituary for an abandoned baby, or one which has died from abuse (including abortion). The reality is that parenthood is a demanding, unrelenting job and some people reach the point that, in spite of their best efforts and many legitimate reasons, can’t handle it. If they realize they are a danger to themselves or their kids, the safe haven laws are a real benefit. Good for them.