You don’t tax the money twice, you’re taxing the earnings.
An argument on Harvard’s side is that, in the grander scheme of things, they are part of a process that generates phenomenal tax revenue. The state takes their 40% cut off the top of every $150k CS and IB graduate salary after all. Is that a good enough benefit to let us tolerate Harvard’s pile of gold?
There is a related argument that if society is to be the ultimate recipient of the majority of benefits of a university system, then it should probably be state funded. Just like roads (public) trains (ish) electricity (not any more) and food (private but subsidised).