I actually call BS on the 'women run things at home' thing. In the UK, the Domestic Abuse Act recognises financial control as a form of domestic abuse because what man giveth, he always taketh away when it suits him.
Women might 'run the house' but unless they're the sole breadwinner, it's often by default. We saw that during COVID lockdown - when both working parents suddenly had to work from home with kids trying to learn from home, overwhelmingly, women became the educator too.
And let's not forget that, as the post says, women are excluded from holding the big jobs, but we're also generally excluded from government, which means we don't get a say.