What I think a lot of people don't understand is that it's not about a list of tasks - eg. who does laundry and who cooks and this and that. That's not really the point of being a SAHM because, to a large extent, you can make those type of tasks last as long as you want. Anyway, one person's concept of "all the housework'" will be very different to someone else's.
The real "work" of being a SAHM - especially if you have quite a few kids - is that you can never walk out the door without either having one or more of them with you, or having first factored in where they are, what they're doing, etc etc.
If you are a working parent with a SAHM, you never have to worry about this. You can walk out the door hands free and ficus in something else for x number of hours. You never have to worry or feel guilty about walking out the door. You never have to worry if they're not happy in the nursery or don't want to go or are ill. You never have to worry about what you're nanny is doing if you have one, or if she spends her whole time on her phone to her boyfriend or whatever. School runs, school holiday plans communication with schools, all homework, clubs and activities - covered. Not by a person who just sees it as a job. But by a parent who loves them unconditionally and will go the extra mile. A mum knows instinctively if they're anxious about something, from day one and through school. It's consistency. You can never pay anyone enough to be as in tune with your kids as their own mother. This is the whole point really.
Tasks like doing the vacuuming can be done by anyone. No SAHM I know thinks of this type of thing as defining her role. You can outsource housework. But some families, where the means is there, prefer not to outsource the 'being there'.
We had 4 DC with roughly 2 year gaps between them so it was over 10 years between having the first and the youngest one starting reception. They were all in different schools at different times and with a London traffic, some days I might not get back from the school runs until almost 10am, only to need to be out again for pick up at 2.30 to get there for 3.30 and get parking. My kids did a lot of things after school and frankly, I couldn't have paid someone enough to do it all. Also, nannies are never going to be across the homework as I was, especially when they had 11 plus exams or other exams. The school run was hellish in some ways, but looking back, that was when they often opened up about friendship issues or other worries they had moving though school. Even in the hours between school runs, I was generally doing something for one of them. That's how it was. So it's not about housework, it's something else and much more than that.