"I get a job. My job offers health insurance coverage, which most do now. I pay a small fee (<$200) per month to get the coverage. If I get hurt I go to a doctor and the insurance covers the costs in full, so long as they accept that insurance. How is this not ideal? What would be better for the tax payer?"

How about just being able to pay that 'small fee' without having it tied to an 'employer'? The 'employer' is normally paying a lot more than your share, so this 'benefit' just means craploads more money going to the insurance company instead of your pocket to make your own decisions with.

"Covers the cost in full"? Really? Rarely, unless it's something extremely basic, and you've got some excellent plan with an extremely low deductible. Which it sounds like you might - for that $200 you're paying, the employer is probably kicking in another $600+ (wild estimate based on past experience and discussions with colleagues).

Being able to have basic medical necessities provided to you should not be dependent on whether you're 'employable' (and 'employed') at any particular moment in time.

"Employer-provided" health insurance is one of the worst aspects of the mess that is healthcare in the US.