Companies who don't deliver as per agreement would find their business shrivel.It's more the idea that private insurance will weasel their way out of paying for needed treatments and care. It's happened to me, it's happened to some of my clients.
Consumers would either use the single payer system, or find a better insurer.
But insurance isn't the only Plan B...there's also concierge health care & even
ordinary fee for service.
The only people who'd use private care would be those who find the single
payer offerings lacking, eg, unacceptable scheduling delays, procedures
refused. Let's say I want horn implants or booty enhancement. Government
would never cover such things. But I should be able to buy them privately.