Just touching on your previous post, if you think women are not "gatekeepers" you must be either deluded or ignorant to the dynamics of sexual interactions. Women are most definitely the gatekeepers in sexual interactions, everywhere you go clubs, bars, in public men are encouraged by social dynamics to make the first move, break the ice etc. I would take your argument that men can say no too if that interaction was a lot more balanced. If it were women approaching men at the bar, when he is standing with his friends in the club, buying him drinks and asking him for his number or to go back to theirs etc a good 99% of the time then yeah men can be considered gate keepers. When men do this they risk rejection, embarrassment with the women taking no real risk at all. Sex doesn't come easy for guys but it does for girls. But it is not, never has been either since the beginning of humans, it has always been the male working for the affections of the female and the female not working at all. It's all throughout nature, males fighting for a female even in female dominated species like spiders a male must come and first tap a rhythm and then almost coerce the female (which if shes not interested will end in death). I'd say once dating then does the dynamics change and favour the male
Saying someone is deluded or ignorant isn't the best way to start an interaction. I didn't say women aren't the gatekeepers, I refuted that it's 100% "natural". It's not, it's the result of social conditioning and the different expectations put on women then men. As a society we've decided sex outside of a committed relationship is bad and should be discouraged but we really only discourage women but reward and encourage men. It's illogical to have a system in place that actively punishes someone for an action and then claim them being resistant to that action is natural. Even if one group is naturally more resistant, in this case women resistant to sex, the social structure in place magnifies that.
To put it in perspective, imagine if someone offered you a stick of gum and then when you accepted several guys punched you in the face justifying it by saying it's "easier" for you to attain gum, couple days later someone else also offered you gum and same thing happens, and this cycle repeats a few times. Eventually, you wise up and the next time someone offers you some gum you reject the offer and then everyone around you claims you just naturally don't like gum and cites your rejection as "proof". Obviously you'd think that's a ludicrous claim because you clearly are rejecting the offer because you don't want to be punched in the face again not because of some natural proclivity to dislike gum. Same thing with women being the "gatekeepers". Women aren't naturally more prone to rejecting sex with men we want to have sex with; we just don't want to be punched in the face (metaphorically and sometimes in reality).
As for it being easier for women and men having to risk approaching a woman, there are a few things you're not taking into account:
1. When it still happens women being approached at a bar tend to be young women. You're not taking into account that it's not nearly as easy for a middle aged woman to attract a man especially when she's having to compete with women half her age which brings me to my next point.
2. Men in general have a longer shelf life and are able to attract desirable partners for a longer period of time and also tend to have more avenues of attraction (looks, money, being funny, etc.). So while it's easier for the average 20-23 year old woman compared to men, over a lifetime the scale strongly tips in men's favor. Particularly if we account for desirability of the partner.
3. You're comparing apples and oranges because you're comparing a man offering sex to a woman he's sexually attracted to (at least enough to get it up) with a woman being offered sex by a man who could make her wet or leave her drier than the Sahara. A more accurate comparison would be to compare the difficulty of a man attaining sex with the difficulty of a woman getting a man she wants to have sex with to approach her.
4. Probably most important, in the age of Tinder men don't even really need to physically approach women any longer so that point is quickly becoming moot if it's not already. Sure a guy can still wind up being rejected but sending someone a message on an app and being rejected has much lower stakes than having to approach someone in person. This also evens up the scales somewhat because both the man and the woman have to "approach" the other especially in apps like Tinder.
As for the interaction being unequal, I'd argue the lack of equality is largely caused by women being expected to be gatekeepers because that discourages the woman being approached from accepting an offer she'd like to accept which increases the man's chances of rejection. There's also the fact that even though the initial approach may be less favorable to the man because he has to take the risk of approaching (which again is becoming less of an absolute requirement) the overall interaction of: offer of sex, acceptance of sex, aftermath of sex is skewed against the woman because she's the one who'll be punished if society (or some parts of it) decides the sex wasn't appropriate (not in relationship, she was too easy, one or both in relationship, etc.). If we're going to say women should be expected to be the gatekeepers because the scales are uneven when a man approaches then I think it's only fair we expect men not to make the offer in the first place when an acceptance has a strong likelihood of backlash for either party since once the offer is made the scales are unfavorable for the woman.
Finally, there's the issue that you're focused on a very specific interaction: man trying to pick up woman in bar/club. However women aren't expected to just be gatekeepers when being approached by random men. We're also expected to be the gatekeepers when we're already going out with a guy. If the reason women should be gatekeepers is because of the risks men have to take in an initial approach then that shouldn't apply when the risk is no longer there. Yet it does so the risk men take on in approaching can't be the reason for expecting women to be the gatekeepers.