I should note, I'm writing this from the confines of my cubicle. Ball and chain attached.
If mine and my wife's schedule is relatively open then it would take a very healthy income to even consider that my time is more valuable than making dinner for my family. I enjoy cooking, and in some ways I enjoy cleaning too. I'd hate to lose that just for simple convenience.
However, if our schedules were busy and making dinner, getting the house cleaned, or shuttling kids around was legitimately hard to balance then I'd probably start to consider the option around $750k.
I could see getting a regular cleaning service at $250k, some part time nanny support around $500k, but a full-time nanny to clean, cook, and babysit would take $750k and crazy schedules (mine, wife's, kids) to justify.
Again, this is a pipedream for a guy who has to be on site with his team everyday, and I don't own my own business. I make good money, but I don't suspect I'll ever get to my higher threshold.