For those in that boat there is a good chance it eventually bites them in the rear. The issue is complex and controversial though, for reasons you cite and others.

Feminism as inverse gender-typing covers more ground, too. I tease my wife she will make an excellent little Republican wife, because she frequently complains "liberated" countrywomen react in confusion or outright horror when she says she would love to be a stay-at-home mom were it financially feasible. They just cannot conceive of womens liberation meaning just that: Self-determism, not dragging wommen kicking and screaming into professional, sometimes even nonmaternal, roles any more than it was right to drag them kicking and screaming into kitchens and bedrooms. The only rational, truly egalitarian, side is they advocate stay-at-home dads no more; all childrearing becomes superfluous at best and a menace at worst.

The sole saving grace is it may be generational: Self-conditioning against bearing and similarly conditioning children suggests its life expectancy is ~75 years.

Another typically neglected aspect of paternal rights is that if they exist at all the question of precisely when a person BECOMES a person is highly pertinent. There again the deck is stacked: Complaints against men impregnating then abandoning women, even COERCING abortion, are common, but if any man dare say, "do NOT murder my child!" suddenly it is exclusively "a womans right to choose." Logically, deciding whether to bear a child once conceived is no more or less any individuals exclusive right than its consequent rearing is their exclusive responsibility. It is manifestly unjust to hold anyone accountable for any decision in which they had no role (i.e. where abortion is legal compulsory child support is taxation without representation.)

Note: That is neither an argument for NOR against either abortion or child support, only for consistency. If we hold men responsible and accountable for their children, with great responsibility comes great power. For my part, I agree we SHOULD hold men responsible for their children, with all pursuant rights and authority. The crux of the problem, of course, is everyone has two parents, so responsibility, rights and authority are jointly shared, making occasional conflicts inevitable. As a society, for good or ill, we generally resolve that conflict by granting gestational parents priority: Her body, her choice, and that really changes little post partum.

I doubt that changes soon; anyone suggesting it immediately invites many fierce charges of anti-feminist paternalism, ending all rational constructive converse. Men opposed to the birth and consequent support of their children will still be helplessly on the hook if they impregnate a woman who chooses to bear the child. Men convinced their children are just that from conception and therefore opposed to their slaughter will, like the fetus, be entirely at the mercy of the woman impregnated. In both cases most paternal rights asserted will generally be respected or not at her discretion. As long as physically bearing a child remains the exclusive province of women, most every aspect of rearing one will also. Ain't right, just the way it is (with apologies to Bruce Hornsby.)