Does every other human have the right to extraordinarily expensive, often unproven cancer treatments only available at research institutions in the United States? Are we willing to start making cost based decisions on who should die (i.e. should we really be spending hundreds of thousands of dollars keeping those above 90 alive for age related illnesses?)
Everyone will want everything free, but for this to work you have to make uncomfortable decisions. If you put nothing into the system, how much should you get out? Should others with more resources then be able to then buy private insurance for access to better care even though that sounds "unfair"?
Everyone always glosses over these fun questions when they talk about universal health-care systems.
1. Your first point about "unproven cancer treatment" has an overly narrow focus on the edge of medical research. These cases are yes something that needs to be addressed, but they are far from the norm of normal medical care.
2. I've never heard anyone ask for anything free related to healthcare. There is very little truly free care in the US. The conversation here is about price transparency and what is considered reasonable.
As a European living in the US I find it mind-boggling that the richest country in the world does not consider universal healthcare to be a fundamental right of its citizens.