What about all the companies that are self insured though? For example, where I work they are self insured. I go with the HSA compatible plan, but ultimately, they just use BCBS for the provider network and BCBS bills the company for every claim.
Personally, I think the best way to make insurance cheaper is to get the most expensive people off of it. For example, you could drop the Medicare eligibility age down to 55. The vast majority of people under 50 pose very little risk to an insurer and insurers are for the most part only paying for their routine care (and not even all that). That is only 7% of overall healthcare spending (and even that, is mostly people over 50). It's the heart attacks, cancers, knee replacements and so on that are the drivers of healthcare costs, and higher insurance premiums.
For example, in August 2016, I was out riding my road bike over lunch and while I was at a stop light, a lady in a minivan drove right through me at 45 mph because she was looking at her phone. I was, and am, in extremely good shape, very strong and fit, so despite waking up in critical care a few hours later with a subdural hematoma, several broken ribs, a shattered scapula, a spinal fracture, and my skull exposed requiring over 100 stitches, I was out of the hospital in just 3 days, back at work in under 2 weeks, running again in 3 weeks, and starting to strength train again in about 8 weeks. No surgeries and no physical therapy needed. Total healthcare costs to my self insured employer, just under 40k. Had I been in the kind of shape and health that a typical American man is in by his late 50s and suffered a the same accident and injuries, it very well could have been hundreds of thousands in medical bills before it was all said and done.
Point being, even when you take into account the tax increases needed to extend Medicare down to 55 year olds, by getting them out of the private insurance system, most likely, premiums would be cut in half for everyone else.