“Many men take no responsibility for the outcome of random sex.”
Nonsense. Men are forcibly held responsible by the state for the consequences of their sex. It is women who can choose to abandon all responsibility on a whim, not men.
Poor women get most abortions and poor men often have no means of paying. But more than that for the pregnant woman and child, more important is the need of having a husband and father. Once upon a time people knew this and it was why there were shotgun marriages.
So yes women who get abortions are abandoning responsibility for both themselves and the man.