Our local surgery will produce a repeat prescription after a brief call.
I imagine that the US system is better, if you can afford the insurance payments, including the increases as you age, or develop illnesses, conditions along the way, for your entire life or if you very secure job with excellent benefits packages, etc.
Clearly, if you are health professional, like pramspotter, you also benefit from the US system.
Therefore, if you can afford it, it is better.
Tragically, many people cannot.
It is not irrational to prefer the US system, as AtheneNoctua does, no less than it is irrational to prefer 5-star restaurant quality food. We can't all afford that every day, however.
What I think is indefensible, however, is that the US spends more per capita on healthcare than than UK, yet only those who can afford it can truly access the effects of that spending. At least in the UK, everyone "benefits" from the government's spending.