Harvard FAS Cuts PhD Seats by More Than Half (opens in new tab)

I would say that this is one clear purpose of Harvard-tier institutions, but that they do also produce valuable research, train educators, etc. as does any other university. Your point explains the "elite" part of elite universities, but they do also generally function as universities as well.

"The Organismic and Evolutionary Biology department will shrink its class size by roughly 75 percent to three new Ph.D. students, according to two professors. Molecular and Cellular Biology will reduce its figure to four new students, and Chemistry and Chemical Biology will go down to four or five admits, one of the professors added."

Do you really think that is the purpose of those departments?