What I'm suggesting is that the proven private sector model is one where employers are simply not involved, not a part of the equation. Private insurance purchased on the individual market. That's exactly how it works in Switzerland, the Netherlands, and also how it works in Medicare Advantage (seniors directly buy their insurance plans using dollars they theoretically set aside over the course of their lifetime through Medicare FICA taxes).
The most practical way to get there, in America, would be to either enact Medicare Advantage For All, or to tweak the employer mandate to only include ICHRAs rather than group health insurance. ICHRAs are employer-sponsored funds (in lieu of employer sponsored insurance) that the employee-beneficiary uses to buy health insurance on the individual market.
I'm going to call you on this point, because what you're hinting at, whether you realize it or not, is that employers need to step up their medical care spend management game, which if implemented, looks damn near dystopian. As someone that works in insuretech, the number of times I've raised concerns about revealing too much about the shape of medical spend to employers is scary to quantify, because once you start going down that road, it isn't that far to "huh, 20% of our workforce is 80% of spend" hrrrm...
We do not want to be going down the road where employers are singled out as the appropriate optimizers there.