There's a lack of equivalence in the time requirement. For a woman, the cost of sex may be shaming(this is more a risk in closed environments such as a school but less of a risk in a more open environment like a big city), pre-maintenance, and post-maintenance.

Whereas for a man a commitment implies a long time and a possible significant financial burden. A burden that can be enforced legally. So a man could be forced to a commitment via in the past a shotgun wedding or via the courts child support. Men in that case are not so much the gatekeepers of commitment but forced into a lifelong commitment of some degree.

Most of the time women want commitment from men they already would have sex with. Except in rare cases of obscenely wealthy people like Anna Nicole Smith instances. Women like casual sex and commitment with high status males and will tolerate the casual sex without the commitment such as with rockstars.

A man who offers commitment too early shines flashing adverse selection warning signs. If a man offers commitment too early it signifies that the man is low value. A man cannot use commitment as a carot in the same way a woman can unless he already is semi-committed to a woman and can use the commitment to dangle the women along. Perpetual engagement.

If women valued commitment then one marker would be prostitutes offering discounts for multiple sessions(they do offer discounts for longer time) but package deals are not common.

Women want commitment from men that they would already have sex with except in cases where the man is much higher status than them.

So woman being the gatekeepers to sex is this big honking gate and then within this gate is this smaller gate that men run which is gatekeeping commitment. Then there is this side gate where men actually are the gatekeepers of commitment. Only once men have passed the gate of sex do they operate the gate of commitment.

It's more like commitment is part of the package deal. Women are the gatekeepers and commitment is part of the package that men can offer along with status and looks to get past the gate. Their are some women that do value monogamy and not just monogamy in name only("I don't care if he cheats as long as he's honest about it or doesn't get caught").

Their are some services to sell male commitment shows like the Millionare Matchmaker, dating sites, etc. but the commitment has not value without the status and the looks unlike the sex that females offer.

Anyways there is no equivalence between the two gates. Men being gatekeepers of commitment is more like a consolation prize.