Well, yeah. The root of the problem isn't single-payer vs. out-of-pocket. The real problem is too many people competing for too little doctors and hospital beds.
Making it centrally-funded won't magically warp new doctors from hyperspace. It will simply shift the pressure from prices to waiting times.
The working solution would be to reduce the bureaucracy and make it easier to open new practices, ban anticompetitive behavior by hospitals and address the residency spot bottleneck. But nope, nobody is suggesting that. We keep fighting about the most fair way to split 3 beds between 10 people.