Please OP, use the fresh eyes your friend's devastation have granted you, and look again at all the things you are accepting as gospel. Try to review things he has said to you from a neutral standpoint, applying no judgement or emotions, just logic.
Something that has jumped out at me - money. Two things you've posted, the source of which can only have come from him:
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"I couldn't care less what he earns. He's self employed and doesn't pay himself too much because he doesn't need to."
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"He's not paying himself any less than he did while they were married. He has been financially responsible towards his family. He's not tried to screw her over."
When you say 'he doesn't pay himself too much', what do you mean? Do you mean he doesn't earn much, or that what he earns is somehow retained by the business? Not knowing the nature of his self-employment, it's difficult to know. So the scenarios I could think of are:
If he had set himself up as a limited company, it is tax-efficient to take a smallish wage as an employee of the company, and a larger dividend as a director of the company. But wage or dividend, it's all income to the same person.
If he is a sole trader/contractor such as a plumber or an IT professional, to pay himself a small amount he either has to charge his customers not very much per hour, or not work many hours. You've said he's a workaholic, so (assuming all those hours he says he's working he actually is working) it would have to be that he doesn't charge very much. Why would he do that? Only two possibilities - 1. Charitable, or 2. People would not pay any more for his work (artist/musician/just not very good at whatever he does?)
Now the second half - ' because he doesn't need to'. (And from the second statement above, he 'didn't need to' throughout the marriage either.) That's such a loaded statement. We all need to earn enough to pay the bills, keep a roof over our head, food on the table, clothes on our backs. It's one thing to not be materialistic, it's quite another to not provide for your family. He was a workaholic, not pulling his weight domestically - AND he wasn't even bringing home the bacon from all those hours working 
. Generally people choose to earn less (by working less) to have more time with their family, but as a workaholic that wasn't the case here.
Can you see the lack of logic, OP? Especially in the earlier years, children are expensive. A bigger home than you'd otherwise need, a bigger car, food, toys, clothes and shoes constantly being outgrown, school uniform - my god they're expensive! If you're in control of how much you earn, you maximise it, because it's tough enough raising children without being poor to boot.
So think about it OP. You termed it as 'paying himself' rather than 'earning'. Again, loaded words. 'Paying himself' is about choice and control. It's one thing to make that choice for yourself, quite another to impose your choice on your dependants. Is it really his choice to work so many hours for such poor reward? And if it is, why is that? Because I can see no reason at all. I think you need to dig a little deeper here.