This is why countries like Switzerland require everyone to buy insurance. The system doesn't work if everyone freeloads.
(I guess we would still call Switzerland socialized, since the insurance prices are heavily regulated, everyone is basically in the same risk pools, and subsidies are given to those who don't meet thresholds)
Isn't that what Universal Healthcare does? They obviously charge premiums, but they are a percentage of income that goes all the way down to 0.
Universal healthcare takes healthcare from being a concern to companies at all, and now they can just hire who they want for however long they want. It also makes the labor pool much more fluid, and makes low end jobs much more viable (morally and economically).