I think that because it's "free", people are probably generally more inclined to make use of it even when not totally necessary. But I also think it's not enough to cause any major problems, and I also think that allowing everyone to have an equal chance to have proper health care far outweighs the (relativly small) added cost of the general "overuse" of the system.
Or is it that once it becomes available to everyone "for free" that the demand goes up, so...
Then so does the cost, and so then goes the taxes?
It eventually gets to a maximum point where the price has gone up via taxes, so then the quality suffers?