That's what high limit medical insurance is for. Unless these insurers commit effective fraud and not provide their service after the fact.
If I could pay for that kind of guaranteed-for-life coverage in the U.S., with $0 deductibles, $0 co-pays, no maximums, no reimbursement paperwork, no excluded conditions, etc., for only 15% of my income, I'd gladly do so. In California, I spent around 7-8% just on my comparatively shitty health insurance + out-of-pocket, which had several exclusions and no guarantee I'd be able to renew at a similar rate if I got sick. So I consider the Danish offer a real deal. Even more so if your medical history has any major blemish on it, in which case U.S. premiums skyrocket to much higher than 15% of a typical salary.
The problem is that we get our health care through health insurance companies.