If you go to dinner with a large group of strangers and you know that the bill will be split evenly, aren't you more likely to order pricier dishes and drinks than you would order if you, and you alone, were responsible for picking up your full tab?
The answer is surely "yes." Let's say that you'd be content to order the pork chop priced at $15, but would get even greater enjoyment from ordering the rack of lamb priced at $25. If you alone were responsible for your tab, you'd order the lamb only if it is worth to you at least the extra $10 that it costs. So suppose that you value the lamb by only $8 more than you value the pork chop. In that case, you'd order the pork chop. You wouldn't spend an extra $10 to get extra satisfaction worth only $8.
But if the bill is evenly shared among, say, 10 diners (yourself and nine others), then if you order the lamb, your share of the higher bill will be only $1. That's $10 split evenly 10 ways. You'll order the lamb.
You might think that this sharing arrangement is good. After all, in this example, the cost to you of getting something you valued more (the lamb rather than the pork chop) was reduced. It became sensible for you to order the lamb.
Look more deeply, though. What happened is that society (here, the 10 diners) was led to supply something that wasn't worth its cost. The lamb was worth to you only an additional $8, but to make it available to you, society spent $10. Ten dollars were used to raise the welfare of society by only $8. (You're a member of society, so any improvement in your welfare counts as an improvement in the welfare of society.) That's a waste of $2.
You are better off, but the group is worse off.
Now look even more deeply. Everyone at the table faces the same incentives that you face. You're not the only person who will order excessively costly dishes and drinks. Everyone will. The entire table over-consumes. The total bill is higher -- even your share is higher -- than it would have been had the bill not been split evenly. Resources are wasted.
Such sharing of our medical-care bill takes place now on a massive scale. It is impossible to see how expanding this sharing will reduce the bill.