One huge reason that things cost so much more here is regulatory compliance. That is fairly minimal in directly government-run systems as the government isn't very interested in grossly running up its own costs in a fully socialized sytem. But with independent contractors, sure, make them document everything in quadruplicate and check 187 checkboxes in a very clunky inefficient mandated electronic medical record system for every patient visit and spend billions and billions of dollars in complying with arcane HIPAA, JCAHO and CMS regulations. (Note that the one fully socialized system in the U.S., the VA, is exempt from all of that.) And then fine them/reduce their reimbursements if they don't jump through all of the hoops properly. It saves the government a little money but costs the healthcare system as a whole a fortune.
The whole bit about "poorer outcomes" is mainly a combination of cherry-picked facts and factors well outside of the control of the healthcare system. For example, infant mortality in the U.S. as reported by the "socialized medicine is teh awesome" crowd is higher than most European countries. Why? We have a very different method of counting what a live birth is than Europe (they count a lot of extremely preterm births as "nonviable stillbirths," we do not), and when we use the same metrics as they do, our stats suddenly look a bunch better. Our survival rate for extremely preterm births is #1 in the world and also cancer mortality is very low as well. You don't see them touting those stats though. We do have some issues with certain populations essentially ignoring their health (such as having a higher smoking rate than most of Europe) but that is a cultural issue and has remained very resistant to even massive interventions by the healthcare field. You can't blame the healthcare field in the U.S. for that.