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.