This is not true for most universities around the world. Only wealthy ones in first-world countries. All of my father’s academic colleagues in Mexico use Sci-Hub daily, and rely on it for access to literature.
But beyond that, there are paywalled journals which Harvard does not subscribe to. There are journals which the University of California does not subscribe to. (Or pick your favorite university, and there will be some paywalled journals it does not subscribe to.) Almost all are on Sci-Hub.
Moreover, even in the USA/Europe, there are many researchers who are not affiliated with any university, and many laypeople who look up scientific literature from time to time. For instance a great many paywalled papers are directly relevant to working computer programmers, but not worth $35/paper + bureaucratic hassle to evaluate.
