Is it logical to think a system run by the government is going to be more efficient and cost less?
Ah yes, the reason we'll soon have no more antibiotics.
See, there are two problems here: one is that it costs over US $1,000,000,000 to market a new drug, due to those pesky government requirements to demonstrate that drugs are safe before marketing them. This came about, in part, because of the tens of thousands of birth defects caused by thalidomide, but who cares about that? I mean, having a drug that alleviates morning sickness should be worth having a few percent chance that your baby is horribly deformed, right? Why complain if someone wants to market snake oil or something that's poisonous, if it profits them? The government shouldn't be in the business of protecting its citizens' health.
Anyway, antibiotics have been known to have a short efficacy period since the 1950's. Bacteria evolve resistance so fast that you need a steady stream of new antibiotics in the pipeline to keep up with them.
Unfortunately, unlike, say, Viagra, cholesterol meds, or antidepressants which work about as well as placebos, there's not much of a profit in selling antibiotics. Sure, farmers give them to cattle to plump them up, but that's not enough to justify blowing $1 billion on developing a new one.
Hence, it's not profitable to make more antibiotics, and soon we won't have any. That will be sad, of course, because it will have follow-on impacts, like, oh, no transplant surgeries, and, in fact, the risk of death due to hospital infection will rocket back to 1920's levels. As with your grandparents or great grandparents, a scratch in 20 years will have a real chance of killing you, if you get a multidrug resistant infection. Your death will be slow and painful, but at least, no one will lose a profit by curing you with a few pills, and the government won't be able to interfere.
This is the logic of profit without government control. Incidentally, finding new drugs is getting so unprofitable that non-profits such as the Gates Foundation (and the US government) are paying for a lot of drug development. Obviously, this is stupid socialism and a frivolous waste of hard-earned capitalist gains, but whatever. Gates, at least, can choose how he wants to waste his fortune.
Or, just possibly, there's something wrong with the logic of getting the government out of the way? I think HL Mencken put it reasonably well, back in the 1920's: "For every complex problem, there is an answer that is clear, simple, and wrong."