It won't happen, as long as the government still allows private hospitals and doctors to work. Because then the private sector needs to compete with a functioning healthcare system that's essentially free for any citizen. If the expensive private clinic doesn't give you better care than the free government one, you'll never use them. Having universal healthcare raises the baseline above which private health companies have to be, in order to compete. And sure, government healthcare sucks. Sometimes the doctor doesn't even smile at me when I see him. Their equipment is frequently not the absolute latest possible. But they'll see to your cough, set your bones, fix your teeth, check your sight and more for essentially free. Which forces the private hospitals to do it better, faster and for a reasonable price.