The problem is that that is a vicious cycle. The more men shotgun the more women have to be picky. So nobody answers and man have to write to even more women...
Usually this get's "fixed" by limiting the amount of messages men can send. But that doesn't really work.
There should be a system that "punishes" women for being picky and men for being desperate. Maybe publicly show the ratio of received/sent messages, or so?
Tinder has a bit of a mechanism for this: you can only right-swipe on 100 people per day (as an unpaid user). That helps limit the "shotgun" approach to an extent, though it's probably not enough.
I tried the shotgun approach for a very short time once on Tinder. I stopped soon after because I got so many matches from women that I just wasn't interested in or attracted to, and I felt really bad about popping up as a match for them, and then disappearing suddenly, which I've seen women complain about. (Plus I ran into that 100-person limit.) So I only right-swipe for women I have some interest in now.
I don’t want to misinterpret you, so is this what you meant to write?
There's an obvious imbalance in pickyness between the genders. So counter-weight that somehow.
It should encourage being picky for men, and discourage it for women.
So we have to limit something for men, because it's easier to become picky.
What if you could sort people by the ratio of messages to answers? E.g. as a man you would show up more easily in results if you don't shotgun. And as a woman you will stay more hidden if your postbox is already overflowing.
However I strongly assume that most women on those site just are picky. Looking for something they can't find in real life... So the system is just broken anyway, at least for "normal" men.