Either way the family will be making $50,000, only one way their expenses are $20,000 more and the other involves the mother being at home 40 hours more a week, accomplishing more household tasks and essentially returning us to the 1940's.
It wouldn't necessarily be the wife however, as in my household I'm the one earning the 2/5ths and would have little problem being a stay at home daddy/teacher. In fact, being an uber-nerd I have a strong feeling I'll be teaching more math and science skills to my offspring than any educational facility anyway, and having worked as a writer I know I'm going to be teaching far better English skills at an early age than any primary school education will give my kids at a 30:1 child:teacher ratio. So being paid $20,000 to stay at home and do what I'd be doing in my free time anyway, seems like a win-win.
I am just advocating for the child. As parents we're in the best position(mostly) to judge what our children's needs are.