Calling them a 'tax write-off' makes it sound like something sinister is going on - just about everything a business pays to run their business is deductible, and thus a 'tax write-off'.
Do we call buying paper for the xerox machine a 'tax write-off' and thats the only reason business buy paper?
Its a cost of doing business - just like rent, payroll, heat, electricity etc - there is no special 'write-off' for providing health insurance for a typical company.
I guess the overhead of setting up such an organization plus the fact that said corporation wouldn't actually have any revenue are big issues.
Whereas with statutory employees anything the employer purchases in that regard is not included in the tax base for the payroll tax or the income tax, i.e. is basically tax free. Self employed folks are treated better than they were a few years ago (no deduction basically), but that is still a big difference.
The biggest drawbacks to such an approach are that you have to deal with the quirks and rules of your organization -- read the terms carefully -- and that you have to deal with the paperwork from the medical system yourself. That doesn't sound so awful until you experience it. You can find reasonable primary care as a cash patient -- direct primary care is everywhere now, and almost certainly what you want: a monthly payment for someone on call to deal with your issues. Urgent care is generally reasonable, too, being an up front single bill at a fixed price per type of issue. But Lord have mercy on you if you need to visit a hospital. The paperwork is stunning. A couple years ago, I went in for some observation and antibiotics for a couple of days, and came out with a dozen bills, all of which have to be called on, paid, negotiated, and some of which are possibly fake.
John Oliver covered Health Care Sharing Ministries (often called Health Shares or HCSMs) a while ago https://www.youtube.com/watch?v=oFetFqrVBNc