To me, it seems the “dude pays” rule is an homage to the patriarchy but in some cases it’s just a statistical fact that more men than women can casually pay for things without feeling it in their budget, while the woman would just have to decline that date if she had to pay even her share.

Is it a statistical fact? I have to kind of snicker that you used "in some cases" and "statistical fact" in the same sentence. It sounds like you're hedging. Regardless, I was under the impression that most of the income wage gap was attributed to the "motherhood penalty". This would make sense if, for example, you were dating a single mother. Otherwise, single young men and women of the same age typically make the same amount of money. In my area, the gender wage gap between young men and women between the ages of 16-25 is only 5%.

Statistics aside, you don't know how much money your date makes unless they tell you. I would consider that an out of bounds topic on the first few dates.

For things to be equal when disposable income is dissimilar, I think it’s fine of the person with more money pays a disproportionate share, and sometimes that will mean they pay for pretty much 100% of everything.

I think the income differential would have to be staggering (like sugar daddy/momma level) to justify 100%, but that's just me.