Not the GP, but yes I would. The problem is that this is
very hard to demonstrate for several reasons.
First, most analyses assume that healthcare is fungible, so anyone who "has healthcare" is considered to be in the same boat. This is untrue. Most government-provided healthcare systems rank quite poorly in terms of wait times, fatality rates, etc. compared to private healthcare.
Second, it's hard to distinguish the benefit of government medical systems from the benefit of freeing the private medical system from legal red tape. For example, many people cite lower drug costs as a benefit of government medicine. This is not an intrinsic feature of "single-payer" healthcare, but rather a result of the fact that drug agencies in the US have the full weight of the patent system behind them in order to create artificial scarcity and drive up prices. In other countries, since the government both buys drugs and controls IP, the government always has the threat of removing IP rights to a drug if a company fails to provide a "reasonable" price, which simulates actual competition. One could get the same effect by changing the nature of medical IP rather than taking the drastic measure of publicizing drug purchases. That is a utility analysis I'd really like to see.
Third, one must include the utility of having a choice. There are both psychological and practical components to this, but it's better when you're not forced to pay for a service you don't want. I know how good private healthcare can be; just go to a tourist hospital in Mexico or India. Truly an awesome experience. A super easy way to get all the alleged benefits of socialized healthcare (especially affordability) is just to deregulate the shit out of hospitals. A lot of Americans are scared about that because they think deregulation is synonymous with the triangle shirtwaist factory, but it's truly a mind-bending experience how good the healthcare is in medically deregulated countries.