Rather than assuming the level of duties the Torah imposes on men is the baseline, and asking why women are exempt, I want to flip the question around and ask why men are obligated. What gender difference would make these obligations more meaningful to a man than a woman.
I think we should just admit that synagogues (and, lehavdil, churches) were invented to be Men’s Clubs. When the non-Orthodox movements broke that model, or churches did, men lose interest. No matter how liberal or feminist the typical man in their community is, when the clergy is made egalitarian, male attendance falls off. The Conservative Movement’s Federation of Jewish Men’s Clubs has even experimented with a guy’s only service in order to encourage a return of men to worship.
In contrast, when the Enlightenment preached a religion stripped of ritual in favor of direct contemplation and internalization of its truths, men created groups like the Freemasons — complete with Temples, rituals, “deep truths” (at least, back then that aspect was central) and in a male-centered environment. They recreated the ritual laden “fraternal order” outside the context of religion.
It would seem that there are gender differences that makes this format effective for men. Whereas giving women an equal role in rite ends up breaking it. I am not saying anyone is superior or inferior over it. Nor am I even sure what it is about the male gender that causes this effect. All I am noting is the evidence to say there is a particular model of rite and community that is effective in bonding men to the society and inculcating in them its values. And perhaps that’s why we were given more rituals; rather than looking at why women were unburdened from them.
Shul looks like a Men’s Club because it was designed to be one. And that’s a good thing.