In the 1960s, William Baumol (in his book, co-written with William Bowen, Performing Arts: the Economic Dilemma, as well as in subsequent works) noticed that, almost by definition, the productivity in the “services” that required direct human interaction (e.g. schooling, certain medical procedures, performing arts, etc.) would necessarily lag behind the productivity in other branches.
He then warned that this phenomenon could be exploited by political demagogues bent in de-funding public good provision, since the cost of schooling, medical care, etc. would appear to skyrocket compared to other costs, even if there’s nothing strange or wasteful (“inefficient”) about that.

How right he was!  The political demagogues, the whole “neoliberal” assault on working people, milked the “cost disease” to extremes, and that continues unabated all the way to (locally) Scott Walker, Chris Christie, Michael Bloomberg, and (nationally) to Clinton, W. Bush, and Obama.
So, no and no!  The fact that it “costs” more stuff today than yesterday to get a kid through elementary school or to provide medical care to a patient does not mean that schools and hospitals are necessarily wasteful and teachers and nurses a bunch of greedy monsters.  Make no mistake, schools and hospitals may be wasteful compared to some reasonable standard, but the observed “cost disease” does not imply waste.  It is simply a reflection of the fact that productivity in branches of the economy that can be mechanized and automated more easily well, duh, goes up. So a worker in those branches can produce more of the other stuff in less time while the amount of human time required to school a kid or help a patient in a hospital stays about the same.  So, thus the higher marginal product of labor in the stuff-producing branches drives up labor costs (in stuff- or “real” terms) in schools and hospitals as well.
So, this is not a terminal-fiscal-crisis-oh-my-god-oh-my-god-we-must-starve-the-beast-now, but instead something we usually call progress.