In Australia you can go in to emergency for anything, but you'll be waiting until there's nothing more urgent in front of you. If you are triaged as having a trivial condition and you insist on a doctor instead of the triage nurses advice you're in for a looooong wait.

You're spot on about doctor visits not being fun. We also have free GP access and people will see a doctor if they have a reason but most people would rather stay home and rest than go out to the Doctor's just because they have a sniffle.