This is a very rough way to put it, but it's a fantastic idea. Policymakers call this universal healthcare.
These people need our votes, though.
Banning patents sounds good; it sounds like freeing technology from greedy capitalists. But in practice, it means freezing (or at least dramatically slowing) the development of new medical technology.
The Epipen does not "still have an enforceable patent" because there is not an Epipen; there is a series of them. The original design is not encumbered by a patent.
The specific problem with patents and drugs or medical devices is the FDA decisions on what products are interchangeable. The reason drug companies get away with these "minor tweak" patents is that the FDA doesn't see the changes as minor, and so will not permit a prescription written for a new patented version to be filled with a generic based on the old unpatented version.
You can make the argument in this case that the problem is not patents per se, but the interaction of patents with prescription drug regulations. These sorts of "tweak patents" are useless outside the world of prescription drugs.
About the opt-in society, I think it can create rules to prevent the disadvantages you mention; for example by paying a percentage of your salary/profits instead of a fixed amount; or perhaps by taking -free of charge- one sick poor person for every 10 healthy ones that enter the system.