You (and other posters in this thread) are making several assumptions that are not necessarily warranted:
- That the person needing the care will negotiate for it at the time when they need it
- That the person needing the care will negotiate individually, and not via some collective bargaining mechanism
The second point is why socialised health care and insurance companies have advantages over individuals in negotiating for care. An individual probably won't need to go to hospital in any given year, and very few of the ones that will need to can predict what treatment they will need in advance. In contrast, you can statistically work out roughly how many people in a country will need what kinds of treatment, with quite high accuracy. Negotiating to pay for them all together puts you in a much stronger bargaining position.
The big problem with this debate is that it conflates a whole range of choices in a single socialised medicine vs private medicine debate. In reality, there are a lot of points on the spectrum, depending on:
- Are hospitals owned and doctors employed by central government, local government, or private enterprise?
- Are medical services bought individually, as a private collective, at a local government level, or nationally?
- What mechanism is in place for judging the quality of care and for the payer to select between providers?
- Is payment by individuals based on need, ability to pay, or something in the middle?
The question of what role the free market plays is complex. Obviously, you can't have people who have just suffered a heart attack shopping around for the best value ambulance to take them to the best value hospital. But you can have, for example, a central government buying medical services for all citizens (which typically counts as socialised medicine in these debates), but having different medical centres competing for the business, especially if they're allowed to take private patients as well so that they can stay in business when they don't have the majority of the government contract.