Because single-payer systems have enough bargaining power to get much better deals from drug companies both theoretically and empirically. A few years ago when I was taking a health care policy class and actually looking through the stats, drugs cost ~2X in the US vs G20 averages. Not sure what it is now, but I would be very surprised if it had shrunk.
Others: having one predominant type of insurance nationwide cuts down on administrative costs (figuring out different plans costs consumers and hospitals money, these costs aren't minimized by competition), the cost of 1/sqrt(n) risk, and "bandwagon" risk (if a market plan is particularly advantageous for any given group of people, those people all sign up and "sink the ship," whereas national boundaries largely prevent such movement).
It's one of the reasons for this:
https://en.wikipedia.org/wiki/List_of_countries_by_total_hea...
Others: having one predominant type of insurance nationwide cuts down on administrative costs (figuring out different plans costs consumers and hospitals money, these costs aren't minimized by competition), the cost of 1/sqrt(n) risk, and "bandwagon" risk (if a market plan is particularly advantageous for any given group of people, those people all sign up and "sink the ship," whereas national boundaries largely prevent such movement).