Karl, it certainly does happen. I know of three examples myself (at least). And while I wouldn't do it myself, I can also say that every one of those fathers was willing and knew the risks. In fact, one doesn't even know he is the father of two teenage girls... so that is how much attention he paid...
You say men can't be expected to abstain, they have hormones. But so do women, they also get pregnant without planning to. So the problem for you, seems to be mostly biology?
It's swings and roundabouts really. If a man gets someone pregnant, he has made his decision and has no further say. But also, he could just run away, and (or not) return several years later.
I disagree that women don't acknowledge it, all know they could do it if they wanted to, although most don't. But let's be honest, many men are not too shy or bothered about who they give it away to...