You are probably under-estimating the size of Harvard. That isn't to say that large organizations tend to be ... well large organizations, but Harvard is huge.
You are probably over-estimating the size of Harvard. It’s not that huge for an R1 institution. Obviously, they have to pay huge money for cutting edge equipment and high salaries for top talent. But I don’t think that Harvard is protected from any administrative bloat so endemic in higher education. And since Harvard commands so much money the problem can theoretically be much worse than with state universities and LACs.
The specifics of administrative staff at a place like Harvard are doubtless different from your typical comparable company (What does a Dean of $X do???) but probably pretty similar in principle. Maybe less directly influenced by market pressures but you just can't operate a large organization in the same way you organize a small one.