This solution has potential to permanently remove the overhead introduced by "marriage".

You'll gain hours, but not necessarily productivity. Which is a common mistake in management thinking. An extra hour of work out of an assembly line can produce an extra hour's worth of product, there's a pretty clear and measurable extra output there. In software, and a lot of other design work, this correspondence is less precise. For Cody the Coding Machine you may get a real extra hour of output from him. From many others, you'll find they extend their breaks from 15 minutes to 20 minutes, lunch goes from 30 to 45 minutes, and the extra time is taken up by meetings or answering emails.

The productivity doesn't come from extra time, it comes from alleviating stress and increasing the ability to focus. If my thoughts at 2pm are, "Wait, is it my day to pick up the kids? I've got a 3pm meeting, I've got to text the wife to let her know I can't get them today." I'm unfocused. Childcare, consequently, can relieve me of those thoughts. Same thing with bringing in food or having medical and fitness options available. They relieve some stress/unproductive time spent thinking and planning, which will hopefully improve productivity overall, but extra hours recovered from this are not necessarily more productive just by being available.