It seems a lot of the argument against universal coverage/single-payer is the belief that people will "use up" healthcare resources just because they can and because they don't have to pay directly for it. While this is a concern to some extent, it is hardly a fatal flaw, and people already
fraudulently consume healthcare resources in the US (such as the homeless guys calling the ambulance in propita
's example), so things like that aren't going to change much if we switch to a single-payer system.
change is people having access to preventive care, and individuals with chronic conditions being better able to take care of themselves, both of which lead to a reduced reliance on emergency medical services, which are expensive and often very strained.
There will always be abusers. The presence of abusers does not present a valid argument against implementing such a system in the first place. You do what you can to mitigate abuse, you don't just throw out the whole concept.