In some respects correct, in others, very much not.
Yes, the increase in higher ed is 100% administrative bloat. The cost of teaching per student has not risen, and the cost of research (easily 1/3 of the mission of all but the pure teaching colleges) has risen, but not at the rate of of overall university cost. Some of the services are nonessential, but many are not (e.g. today's veterans, veterans children, and first generation students often do require additional attention, and those do add costs).
The real costs come from three sources:
- Reduction of public support as a % of higher ed budgets
- Abandonment of trade schools
- A proliferation and/or growth of colleges following WWII
The first of those (not so oddly) correlated with the late 1970s resurgence of conservative influence in the wake of the school integration movement and Vietnam protests. The second was a consequence of growing commercial globalization, and an unfortunate consequence of the Civil Rights and Gender Equality movements (people, understandably, wanted their kids to have access to the best opportunities, and not be "stuck" in what was unjustly maligned as a "lesser" blue collar life). The third was powered by a combination of the post-WWII GI Bill, and the abandonment of trade schools as a popular path to success, as well as an effort to make education available to more people.
Simply put, colleges outran their viable market, and so began competing on something other than their real value proposition (discovering knowledge and improving minds). They began leaning in to experiences of all kinds, including athletics (which rarely pays for itself, not matter what revenues it generates). With diminished public investment, the only way for universities to fund their offerings was public donations of various kinds, and that requires a whole infrastructure of its own, and that really accelerates the bloat you speak of.
Now, as with any large entity, there's definitely inefficiencies in every university or college. However, the causes are not as unilaterally at the feet of the institutions' mismanagement as your post suggests.