I don't see what the speed of light and observational truths come into play here. I'm aware that people will have sex no matter what, but those people should either be aware of the consequences, or take responsibility for them should they fail to be aware of them. It is not my fault and therefor not my responsibility to help prevent it or pay for the care afterwards.
"Amputate" them from the budget is EXACTLY what needs to happen. If they're cut off they'll shape up and make a difference, if not they'll be homeless and will have no one to blame but themselves.