To answer your question, the way we think of health insurance isn't compatible with a free market system. Insurance pools risk and money to cap your losses in rare, ruinous events. But that's not how we use health insurance. We use health insurance to pay for low-cost, common, certain-to-happen events (blood work, checkups, X-rays, sprained joints, etc.). To borrow an example from the book, imagine we had grocery insurance. Every month, you paid $500 to the grocery insurance company, and you could go to the store to pick out any covered groceries. The market for food would quickly take on all the negative features we find in the market for healthcare. Prices that are crazy and only get higher, minimal competitive forces against low-quality providers, no transparency for consumers, etc.
Market forces are great at lowering prices while increasing quality, but they only work if people personally decide how and where to spend their money. If you give your money to a third party who then makes all the spending decisions, it smothers all the price/demand/competition signals that providers should naturally get. (And which, in a healthy market, automatically put providers out of business when their prices get to high or their results dip too low.)
To borrow from the book again: it seems crazy to expect people to pay for healthcare out of pocket. But add up your premiums. You're probably paying $6-10k per year right now. That's many times more than enough to cover typical healthcare in most years. With plenty left over to buy catastrophic coverage for high-cost low-probability stuff. And in a market where people are making their own decisions with their own money, prices would quickly drop, which would stretch your out-of-pocket dollars much further than they go today. Every $2500 MRI would go out of business, replaced by $500 ones. (We already see this kind of price deflation in the corners of medicine where people do pay out of pocket, namely laser vision correction, plastic surgery, and to some extent walk-in checkup clinics.)