It's essentially the free rider problem. If we want to make affordable healthcare available to everyone then we have to force everyone to pay into the system to spread the risk around and get the healthy to subsidize the sick. It kind of has to work that way regardless of whether we have a single public payer funded by taxes or multiple private payers funded by insurance premiums; in the end the money has to come from everyone.
It's essentially the free rider problem. If we want to make affordable healthcare available to everyone then we have to force everyone to pay into the system to spread the risk around and get the healthy to subsidize the sick. It kind of has to work that way regardless of whether we have a single public payer funded by taxes or multiple private payers funded by insurance premiums; in the end the money has to come from everyone.