Before I get into this, let me say first that economists don't have a lot to say about income redistribution generally. Economics doesn't offer much guidance on whether taxing the rich to help the poor is a good idea or a bad idea. Different societies make different decisions on how much redistribution to do, and that's usually accomplished through the ballot box.
But there is one important sense in which any sort of insurance is a wealth-redistribution plan. And it's a form of weath redistribution that, for the most part, people engage in willingly.
Insurance redistributes wealth from the lucky to the unlucky.
How does this work? Think about your homeowner's insurance. If your house burns down, that's unlucky. But if you have homeowners' insurance, the insurance company is going to pay a big part of the replacement cost. Wealth has been redistributed (from somewhere) to you. And where does that wealth come from? People usually figure it's coming from an insurance company. And this is right, sort of, except for the fact that corporations are just legal shells that allow people to transact. The corporation's wealth has to come from somewhere. So where does the wealth come from?
Now think what happens if your house doesn't burn down. That's lucky, right?. But you still had to pay your insurance premium. And it's the premiums from the lucky that are transferred to the unlucky.
It's wealth redistribution, pure and simple.
So why do the lucky put up with it? Wouldn't they be better off refusing to subsidize the unlucky? Well, yes, and that's why we don't allow people to decide whether to buy insurance after they know whether they're lucky or unlucky. You can't go to Allstate and say "Hey, my house burned down last night. So how about a buy a policy that covered me starting yesterday?"