I am afraid the question makes little sense. Regression to the mean suggests at some time all services will be average. Indeed, at some time all services will be unresponsive just as at others they may be fantastic. Daniel Kahneman pretty much got a Nobel prize for pointing this out. And it’s not a fact for government alone: it’s what happens in human behaviour whether in the public or private sector. The only myth has been that it does not happen in the latter and only the former. That’s as wrong as the question was misplaced.
The question has to be how is the average improved. That’s a different issue.
Regression to the mean means that all services will at some time be average?
Erm, no, the fact that we are surveying all services to decide upon what is the most common status of them (mean, mode or median) means that the most common status will be, umm, the average.
As to how to increase that average that’s simple. We need to use the experimental method that markets allow. Try things out, see how they work better or worse than other methods and then adopt those that work better more generally.
For example, if we wanted to improve total factor productivity (ie, gaining more output for any given set of inputs) then we would very definitely want to have a market based economic system. The experiment of the 20th century proved that to us. The Soviet Union (according to a Paul Krugman essay at least) managed not to increase tfp by one iota in all its long and bloody life. 80% of western world economic growth in the same time period came from improving tfp.
Thus, in order to get more output from any given set of inputs we want to have a market based economic system.
And would we like to have more people cured of their ailments for whatever amount of money it is that we’re willing to put into health care? Why, yes, we would. Therefore we want a market based system in health care. QED.