Imagine that a restaurant were to announce to 100 diners--all strangers--that they would be splitting the tab. If a diner wanted to buy a $50 glass of wine, it would only cost him $0.50; on the other hand, it would also cost the other 99 diners $0.50. If the diner decided instead to have a $2 soda or a $5 glass of wine, he (and everyone else) would pay $0.02 or $0.05, respectively. What would people under such circumstances end up ordering, and what would they pay for it?
Many people would dislike being in that situation, particularly with strangers. While some groups of coworkers will routinely agree to split restaurant checks without niggling over whether everyone's food cost the same, they generally don't want to be seen as unfair by their fellow workers. They will thus either seek to avoid spending substantially more than everyone else, or else offer to pick up a larger share of the total tab. In a group of strangers, however, such pressures will often not apply. If it seems as though many diners are going to have to pay $10 for other people's wine, they'll likely order wines costing around that much themselves, thus pushing the total up higher.
Given a choice, most people would rather dine in a restaurant which allowed them to simply pay for their own meals, than dine in one in which they are required to pay for everyone else's. While there are some all-you-can-eat smorgasbord restaurants, the variety and quality of food is nowhere near what could be found at many pay-for-what-you-eat ones, and for good reason. Customers who are allowed to select expensive food and drink without having to pay for it are apt to do so, even if they wouldn't be willing to pay for the cost of such food and drink themselves.
On the other hand, if some restauranteurs could get the government to require all restaurants to engage in "cost sharing", they'd make out like bandits. They'd be free to put whatever expensive and profitable items on the menu they wanted, secure in the knowledge that some people would buy them and everyone would have to pay for them. At first they might be limited by some restaurants' ability to limit their selections to only cheap ones, but if they could convince the government to require that all restaurants carry expensive foods and beverages, they'd be rolling in gold.
A couple more observations: (1) customers of a cost-sharing business will often find the price to be much greater than what they would want to pay for the goods or services they expect to receive; (2) the quality of goods and services will often be higher than what customers would have wanted to pay for.
Presently, much of what is called "health insurance" is in large measure really cost sharing. A single-payer health system would represent an even more severe form of cost sharing. Fundamentally the only way to get prices under control without restricting people's choices is going to be to increase the extent to which people pay for their own choices. Otherwise prices are guaranteed to increase exponentially until there is no choice but to ration services; rationing services will limit prices, but the variety of affordable choices will be far below what it would have been without cost sharing.