Private businesses are fare more wasteful, fraudulent and abusive than are Medicare, Medicaid and VA healthcare. Indeed the government is far better at catching these abuses than private business is: private insurance is defined by it; employers administering it are characterized by its incompetence version, gilded with plenty of scamming.
Public health financing in the US is far more effective per dollar than is private. Even apart from the profit collected by terrible insurers, even before considering the public finances far more unhealthy people.
Indeed all of the many Obamacare cost studies by qualified orgs say it's more cost effective. It's primarily designed to reduce public health budgets, though sold on many other benefits.
Everything you said is exactly backwards. Especially the part where the "existing relationship" with one's employer is somehow the correct way to get better compliance with healthcare policies. That relationship could also be used to insist your kids do their homework: your boss as your kids' boss - how about going over your spouse's credit card bills along with the monthly department budget, too?
You're talking from pure ideology, ignoring the actual well established facts. You're devoted to corporatism, though its practice rips apart all the values you likely insist your ideology enshrines. Try looking at the real world, not the one sponsored by your media chaperones.