Structurally, if the average professor graduates 10 students over the course of their career, half of which go to industry, then an institution with a given prestige level will send 5x as many graduates to academia as it has slots to hire professors.
So just from pure statistics, if everyone is trying to hire for new faculty jobs PhDs from the most prestigious institutions, one should expect the average PhD graduate who goes into academic to get a job at an institution about 5x less prestigious (one a percentage basis) as the one where they got their PhD. (Hiring is of course more complicated than that, but I think you don't need to make a lot of assumptions about the professor hiring process explain the data in the article).
It's not exactly a pyramid scheme design; there was significant growth in the total number of professor jobs, due to population growth and increasing college attendance rates. And in many fields, there exists high demand for PhDs for work in both industry and government research labs. But these statistics mean that only top schools have the option for a large portion of PhD graduates to get professorships... And I don't think there's any realistic reform that academia could make to change this reality.