Can they somehow extract this back as a tax deduction? The parties are remarkably willing to negotiate, whereas your mortgage provider won’t move very far at all if things get sideways. If they aren’t, I’m certain there are ways to financially engineer things to recoup at least some of the “loss.”

Most US taxpayers can deduct medical expenses which exceed 10% of their income (subject to some limitations).

This can be tax deductible if you use HSA (Health Savings Account)

They would have listed a charge for at least $67,957 if that's what they were tendering to the insurance company. Uninsured people do not get negotiated rates which are usually discounted. The final bill might have been lower if they negotiated. A lot of hospitals will lower the bill and then include that number in the amount of "charity" care they provide.

'What would they have charged the family if they were poor and uninsured?'

Probably a lot more

Do you work in medical billing? My experience is just the opposite, they try to extract marginal costs from those people.

I don't but have a cynical view on this based on experiences several friends have had. There are people who will question the charges and try to work something out. But there are also those who feel like there is no option for them so that dialog does not take place and then the debt gets sent to a collection agency and things just get worse.