Hmmm… Waiting lists aren’t an universal problem in countries with a socialized healthcare system. Canada and the UK are notorious for them, but I’m not aware of any long wait in France, or in say, Germany.
Healthcare isn’t a “good” similar to most others. The demand is very unelastic. If you hand out free cars, I’m sure there will be long waits. But free heart surgery won’t have the same appeal.
Of course, I’m sure that there are people who will pay a visit to a doctor ot take drugs though there’s no need for it when it’s “free”. However, besides the fact that many people don’t like much seeing a doctor (even when they need it), healthcare is “free” or “cheap” for all insured people. Being covered by a public healthcare system or by a private insurer has the same result. Once you’ve paid your taxes or your insurance premiums, healthcare becomes “free” or “cheap”. The american with a medical coverage is exactlty in the same situation as a british or Swede. An universal public healthcare system just gives to more people the opportunity of “consuming” “cheap” medical care, it doesn’t create it.
A problem is that healthcare rarely is “rather costly”. In most cases it’s either “mostly free” (when you’re insured under whatever system) or “mostly unaffordable” (when you aren’t).