But it’s not company owned housing (the premiums they pay to the insurance company is cash out; they don’t get any part of it back as they would if the insurance company were company owned).

And compensation doesn’t have to be “no strings attached” to count as compensation, especially if it is something you were going to buy anyway. With limited exceptions (e.g. live-in nannies), employer-paid housing is taxable as compensation.

There's an element of control that other posters are getting at here. One of the fundamental tenets of a market economy is that consumers get to make decisions on their own behalf when it comes to how they spend their money. If they're not making the decisions, is it actually theirs? There's a pretty big principal-agent problem as soon as you start saying "Well, that money is being spent on your behalf, therefore it's yours." (Ironically, the same problem occurs on the other side of the political aisle with single-payer, government funded health care.)

This is also related to the point you made about possible structural problems with the health care and education industries. Maybe if the consumer could actually choose their health insurer and provider, and there were no exclusive contracts between those two sides of the market, and no barriers to entry for starting a new insurer (and none other than necessary medical licensing of employees for starting a new provider), and providers were required to provide transparent information about pricing and outcomes, healthcare wouldn't be such a clusterfuck of an industry. These are all basic prerequisites for a functioning market, but none of them are present in health care.