I agree that this would not be an effective argument. I'm sure he truly believes he would do the necessary work.
My DH runs his own business. It's successful but it comes at a very, very high cost to me and the children. He works all.the.time. He leaves for work at 6am, comes home for dinner at 6pm, and then is back at his desk by 7:30pm. That's at least 6 days a week. He rarely has time to throw a ball with the kids. He didn't even take a full day off for the birth of either of our children (took the morning off both times). He keeps thinking it will change, next month, next year etc but he's been at it for more than 10 years now and I don't see a difference (if anything he's working harder).
Along with that personal cost, you have to keep in mind that every blow to the business is a blow to your personal budget. It's a very hard road for the whole family and not one I would ever recommend.