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> More people are in favor of universal healthcare than against it.

In the US, you can get an answer in either direction depending on how you phrase the question. When you bring in the fact that this will cost money, people tend to flip. Most people in the US already have healthcare through the government or through their employer, so they don't actually really care enough for anyone to pull this off politically.

> Therefore, we should change the system

I agree, the current system is sub-optimal.

> given the success of universal healthcare schemes throughout the developed world

What success? Most countries with "universal healthcare" A) are poor relative to their demographic-imputed economic capacity B) have low-quality care compared to market-based healthcare systems, and even compared to the worst-of-both-worlds American healthcare system often have horrendous metrics on quality of doctors, procedure wait times, etc.