Right. But if they're spending a disproportionate amount of time on unpaid labor then they don't have as much time for the paid labor. Hence articles like this.
https://towardsdatascience.com/visualizing-womens-unpaid-work-across-the-globe-a-special-chart-9f2595fafaaa Here's one source, but there are many. I'm not saying men should do more work than women, and there's no one size fits all relationship dynamic. If you have a partner that's fine with you earning more therefore she does more unpaid labor and that works for both of you then great. I'm trying to make sense of the OP in the context of labor division.
Nope, statistically men do about 25-30% of the unpaid household labor, including the tasks listed above. So I'm not saying men don't contribute. They just don't contribute as many hours as women.
About 70% of the unpaid labor (including child rearing and household work) is done by women. This is why there's such an overall pay gap - women aren't getting (directly) paid for most of the work they do.