This is an interesting argument.

I could see a rule something like the following: in case of an unplanned pregnancy, the woman must inform the man within the first trimester that she is pregnant, and obtain a written (and perhaps notarized) agreement from him to the effect that he is willing to pay child support. If she doesn't tell him or he doesn't sign the agreement, she will be unable to legally compel him to pay. If she tells him and he doesn't sign, now she knows what to expect, in time to abort the pregnancy if that is her choice.

Probably very few men would sign such an agreement, but the few who did would probably be relatively easy to collect from.