Sure, let's take that up. Say nothing is wrong except for the uninsured.

For the people with problems, it is generally a combination of being too poor and/or too sick (or too likely to get sick) for them to be able to pay for insurance at a premium rate that makes a profit for an insurer.

Somehow or another, you need to get more money to those people, and will have to transfer it from the people who do have enough money to afford health insurance. There are plenty of ways to do that:

1. Raise general income or business taxes and hand subsidy checks to the poor/sick
1a. Or call it a tax credit to the needy, but the effect is identical
2. Ditto on taxes, but hand the money to the insurance companies
3. Ditto on taxes, but have the government act as their insurance company directly (the Medicare model)
4. Command that insurers will cover all people despite their pre-existing conditions, and let the insurers raise rates on everyone else to make up the revenue
5. Take over the whole system and have the government run everyone's insurance.

Granted that you probably find #5 the worst option, but are you really saying you wouldn't be screaming "socialism!" for options #1, 2 or 3??

There is also the problem that this is a dynamic situation. If government creates a system to help those who are stuck due to lack of employer provided health care, then you have created a tremendous incentive for employers to drop heath care coverage and hand their employees a Medicaid application form (as WalMart literally has done). It also creates lots of incentives for the insurance companies to game the system to maximize government's share, which then prompts pressure for heavy regulation and/or government takeovers.

How do you take care of the needy while isolating the private system? It's unfortunately a hard problem.

Frankly I don't like the government heavy options either. The problem is that once you've decided that as a society, you don't want to see people die early of treatable conditions, it gets really hard to structure a system that doesn't have heavy government involvement.

If you'd prefer a society where we all self-insure, and if a middle class family that has "played by the rules" is utterly ruined -- someone dead and the survivors destitute -- by breast cancer or a childhood heart defect (let alone by a genetic predisposition for either!), well, there are philosophical and economic arguments for that. But good luck selling it to your friends and neighbors....