That's because you don't realize you ALREADY pay for everyone else. The problem with the existing system of "we have to cover you if you go to the ER, sorry you could afford coverage yourself for preventative visits" is that ER's cost more and the hospitals bill us indirectly for those visits.
Even if all you're talking about is writing off the debt, they get to write that out of what they pay back to the government. So in the very least of terms, you're talking about paying for others health care through tax dollars at whatever cost the hospital decides. At worst, you help pay for the loss of profit by paying higher medical costs, at whatever cost the hospital decides.
The question here isn't whether you want to help pay for health care, it's how much. Would you rather pay $10/mo more or $1000/visit more? Sounds good if you don't visit the doc often, but that one time you do, it'll crush your bank account.
Some time I think the people in this country are so blinded by our brilliance that we fail to see that all the "lesser" countries around us are beating us.