what I've heard is: in places with single-payer health systems, health care for small problems, while it superficially looks wasteful, pays off in preventing big-problems early, enough of the time, that it functions as an investment rather than an expense.
That's the general assumption, yes, though there's some debate over it. Denmark is currently discussing instituting modest co-pays for some non-emergency visits (currently there are no fees whatsoever, besides your tax contribution). The main debate is over whether this will actually save money or not, all things considered. Evidence doesn't seem to be very strong either way.
