No man I have ever met who has a SAHW, frames it in terms of her getting the cleaning done! They don't want their wives wasting time on cleaning. This is so far from the point it's ridiculous. Just hire a cleaner.
For any man I know with a SAHW, it's the flexibility, balance, energy and time they value. When you have money, your focus shifts to quality of life, rather than quantity of money, basically.
For instance, as my kids have gone through school, you can usually see the ones with a SAHP who can focus on supporting their education, going over and above. Where we live in London, kids are sitting highly competitive exams for prep school entry at age 6. The mums are across this with whole programmes to get their kids into x,y,z schools. Most people outside London probably have no idea. The husbands want their kids to do well and they know their wives are the best person to get them there!
On top of this, if you are a very high earner, you haven't got where you are by working 9-5 or counting your hours. Or debating who does housework and if it's 50/50 or 23/77 or this kind of malarkey! If one person earns hundreds of thousands, they will probably need to travel or work in ways that exceed the 'norm,' if you can call it that. So a SAHP, frees up the flexibility of the other person to pay the school fees, have the amazing homes, trips, opportunities, etc. This benefits everyone. And if you split up, the wife probably still comes away with far more than she ever could have earned anyway. This is where having a SAHP works because the children have 100% attention and the opportunities the money brings. That's why people do it.
However, if there are two people earning comparable amounts, the trade-off will be different because the loss of one income will be much more noticeable.
So I don't know here how much this DH earns. If he's on £300k and expects his wife to get a job in Tesco, he's a tosser, frankly. But if he earns 40k, then an extra £20k would make a difference. So who can say?