OP, the question of who has the money / more money - men or women? is simply answered, you don't have to go by socially expressed beliefs or opinions. Look it up. Look up who has more money in terms of capital, investments, income, earnings - is it men or women? Find out and then we can come back to that point. "Only on mn have I heard" is irrelevant - we don't care what the majority of people (in any particular social group) happen to believe, this is a hard fact, and you can find out.
I have feminist issues with marriage too (and some of what you say strikes certain kinds of chord), which is kind of convenient because in my particular case it worked out better for me that I was not married. However, traditionally it has been the case that marriage has been the legal mechanism that has required men to take material responsibility for their families and many women, now, are / would be advantaged by that.
There are many men who prefer not to take material responsibility for their children, or for the woman who has invested enormously in having them and bringing them up. This is a huge problem that marriage alone can't solve. Society used to take a much dimmer view of unmarried parents - and the disapproval was unfairly distributed, putting far too much of the burden on the mother - but the decline of that disapproval takes even more pressure off fathers to step up.
It would be wonderful if mothers and children had access to some other form of support than some man who used to say he loved her but now isn't really feeling it and is a bit bored by the whole thing and let's face it, families are a hell of a lot of work and a lot of other things are more fun. But as things stand - they don't, really. It's hard to support yourself materially when you have sole responsiblity for children. Again, this is a matter of fact. You can access figures for:
Average salaries (net)
Average costs of living (housing + bills + transport)
Childcare (remember this is paid out of net, not gross, as are your other bills)
And you can have a think about how easy it is to do all that on your own.
Children are to the good of society and I believe that the costs should be shared by society more. In the absence of that agreement, I think society, and law, should put more effective pressure on men to support their children. But this is where we are.