I'm mostly befuddled that he considers 4 hours of time with his child a waste. Feeling unproductive while walking with a stroller? Listen to a podcast. Do audio lessons for some new language. Record some thoughts, since he's a coach he could "write" a draft of a self-help book or something. It's the easiest chore to combine with other things.
There's a strong implication that he wouldn't even be doing this if his wife is wasn't a "physical wreck" after the birth.
You have a small baby, sleep schedules are all over the place, pitching in isn't some chore you do just while she's out of commission, there's a human to bring up to adulthood.