There is a debate to be had. But just as women benefit from women only spaces men might benefit from it too. Because sexual selection always plays a role in social dynamics, especially at that age. But I’m not sure it needs institutions for that, and that also isn’t an argument for men only “good old boys clubs”. More about good male (non toxic) role models.
What you get now are vile role models online that are actively pushing toxic masculinity or even fascism.
I mean it could work. Have one of those movie “fan in an air duct” murder fans and then put a cute animal behind them. Endless supply of the proverbial “lemmings hitting the fan”.