If his wife doesn't work then the 30m of me time becomes even more costly and even more important to clear. Work is often the only reprieve from a very young child. The first year of our child, my favorite thing in the world was to go to work, no matter how shitty the task. The thirty minute commute alone was orgasmic, without the sound of a screaming colicky child unrelenting during day and night alike.
Your wife not working doesn't change that you're the dad when you're off work and would typically (I hope?) be involved in your children's education as well.
Parenting is not the kind of thing where you exchange your labor for money. It's not work in the sense that the parent comment meant it and you know that full well.
> Parenting is not the kind of thing where you exchange your labor for money.
Historically, that really is a big component of parenting. More children meant more money through additional hands being available to work the farm, etc.