Mandatory coverage is orthogonal to the question of whether health insurance is a proper insurance scheme, or some kind of social safety net entitlement, or a utility. The sole purpose of the mandate is to make free-riding on the insurance market unlawful; it's a mitigation for an asymmetric information problem.
Only if you own a car and drive it on public roads.
For all intents and purposes, auto insurance is effectively mandatory for most Americans. It's for a similar reason that many states revoke driving privileges for parents who don't comply with child support.
Texas, for instance, doesn't actually make you buy insurance. You only have to prove that you can be financially responsible for the damage you could cause [1].
Why is this relevant? You made the claim that "The sole purpose of the mandate is to make free-riding on the insurance market unlawful"
The medically uninsured only pose a financial threat to themselves. It's only through laws that make taxpayers responsible for the medical costs of the uninsured that they pose a threat to the rest of us. This mandate won't change anything in that respect. It will just make the line from taxpayer money to person who can't pay for his medical bills harder to follow.
[1] http://www.dmv.org/tx-texas/car-insurance.php
edited for clarity
"Middle man" isn't a dirty word. The health care deals you get in the US are much better with the middle man than without the middle man. Since the insurance companies have so much power, they can (and do) negotiate better rates with health care providers. The cost of paying for your own health care is shockingly high by comparison to the rates the insurance companies would pay on your behalf.
I don't know if this sort of story actually plays out -- I live in a country where the only way to get better health care is to move to a different province -- but it doesn't seem completely implausible.
While both government and private companies are both theoretically incented to drive down costs, practically there is a lot more scope for government to operate the plans in an inefficient way without consequence; on the other hand private companies are primarily incentivised by profit, which does not always correlate with the most efficient way of delivering healthcare.
This is where the nuance kicks in (i.e. big government or small government); a well run government plan would better but leaning on the private sector is a hedge against poor management.
The provision of the law which stipulates companies must spend 80-85% of premium revenues on healthcare expenses are an obvious giveaway: "you're allowed to make only this much money".
The next steps, after this is settled law (i.e., Republicans stop trying to repeal it), are to narrow those margins, then introduce a national healthcare system for everyone which these insurers must compete with.
It makes even more sense than a single-payer system (which eschews the benefits of competition), but you can bet there will be continuing political drama over healthcare for the foreseeable future...
You're subsidizing risk across a large group of people. The chances of something happen to an individual are small, but could be financially devastating. So everyone pools their risk together for affordable premiums.
The answer, I think, is partially politics, but also partly whether you think the competition a system like this (in theory) encourages outweighs the cost of profits.
For health insurance to work as insurance you need the young and healthy to participate and pay more than they'll ever get out of the system, otherwise it's impossible to cover the costs for the old and chronically ill.
(Unless of course you are talking about Medicare then its the most patriotic thing since apple pie).