The question about whether or not healthcare should be a right isn't even the right question to ask.
Consider this example: Most people don't think about whether or not having a smartphone should be a right. Most people can just go and buy one because the costs are so low for what you can buy.
So the real question we should ask is "how can we reduce the cost of healthcare." And there are a few strategies there:
1) Encourage automation in healthcare, from the manufacturing of medicine to the administration of care to diagnoses.
2) Encourage a healthier population. 30% of our yearly medical costs are going towards treating obesity and smoking related illnesses. Illnesses that shouldn't even exist. If we eliminated these things, our spending would be 30% leaner (probably even more) which would enable us to streamline the entire healthcare system.
3) Introduce competition into the healthcare marketplace. Price setting and price capping don't work in the long run because of the inefficiencies they introduce. The most effective solution for high prices is to encourage competition and innovation, and the government is uniquely positioned to do that in the same way that it rewarded SpaceX with massive grants.