Let's just say the average single-payer health plan is like $400 a month. However, there is a $100 surcharge to everyone's insurance because of all of the abusers of the system who don't pay for their health care. So the average person pays $500 a month - $100 of which is due to non-payment of treatment.
It's my assertion that UHC would help this problem in two ways:
1) Under UHC, you are combining the clients of all of the current companies. That can only lower prices because, again, as law of large numbers states, uncertainty is lowered and reserves can be smaller. The bigger the sample pool, the better. But we still have those bastards who don't pay ****. Which leads to #2.
2) Those non-payers now have health coverage and can have a regular practitioner who will examine them on a yearly or bi-yearly basis. This would drastically reduce uncertainty in this crowd, and lower health insurance costs because of prevention rather than treatment.
Of course, this means our government needs to know how to manage money effectively because, unlike with Medicaid, they will actually need to pay the doctors. But I just generally try to have a positive outlook on this issue and I cannot see any negative side to universal coverage.