I don't buy that. Middlemen typically exist to solve some existing market inefficiency, or they exist through corruption and regulatory capture. The latter is a huge problem, but it's not THE problem. Ballooning administration seems to REALLY be the problem all over the place. But... Why is that?
Because there is no competition, and demand has massively outstripped supply. If you want to make money in academic management, you need to build an organization to manage and then justify a high salary to do so. And this is what happens. Huge staffs doing nothing but justifying the boss’ salary have appeared at universities over the past few decades.
