It's not a good analogy because the same medical providers - doctors, nurses, hospitals - would continue to provide the same services, only they'd be paid by a single payer rather than thousands of for profit insurance providers. I wouldn't suggest an across the board instant 30% cut. Some formula can be found that doesn't bankrupt everyone.

So - not Medicare for all, but just a single-payer system paying private insurer rates (or the equivalent), and offering private insurer AV (or the equivalent)?

That wouldn't bankrupt everyone, but it will be awfully expensive for the participants...

I think universal health care will be massively popular with most of the electorate.

Two problems with that. First, UHC might be popular, but paying for it won't be. If you don't slash provider reimbursement and get everyone up to the typical value of an employer-based plan, it's going to be very costly indeed. Second, all the people who have very good private insurance (the ones who would have had to pay the "Cadillac Tax" under the ACA) are going to be very upset to suddenly have to start paying a ton of money for health insurance that's worse than what they had. And that 15-18% is mostly retirees and public sector union members, who are very active groups in the electorate....