The vast majority of SAHPs and part time workers are women.
I'm not suggesting at all that the WOHP shouldn't take any responsibility around the house but logically that probably influences who does the most housework (as one partner is in the house more).
I'd be interested to know the set up between couples that both work equal ish time out of the home.
We have a cleaner and an after school nanny (latter cooks dd's meals 4 days a week) so there's less for us to do tbh.
I do laundry, top up bathroom cleaning, all school admin, sorting childcare (cost is shared), sorting/buying dd's clothes, organizing parties/presents/social stuff, online food shopping, anything that requires forward planning. I probably do more cooking at weekends but it varies one week to the next.
Dp does everything to do with the garden, car, cat, tech stuff (important as we both work from home sometimes), general DIY and arranging for things to be fixed, bins, top up hoovering, anything gross (cleaning mould, plughole etc).
Rest of chores, cleaning and all of childcare, school drops etc are fairly equal.
Being financially independent, not giving up my job and having an equal ish arrangement was a non-negotiable for me. I wouldn't have settled down with anyone on any other basis.