And you hit right upon another issue. Tuition and research grants, because they come from taxpayer dollars, are considered restricted funds. You have to use them for their intended purpose, and there's a list of things you can't buy like alcohol, dorms for athletes, president's salary above a certain threshold.
Commercial patent royalties are considered unrestricted funds, along with endowment and donation money. They are used for a whole slew of things that restricted funds cannot be used for like stadiums, swanky donor parties with tons of wine, renovations to the president's free housing, $55 million settlements for research fraud, etc.
This is why Caltech is so motivated to go after this. It's a huge amount of cash for the toys they can't otherwise buy.
What you say is substantially true, although obviously biased. I would point out a couple of things:
1. I doubt Caltech spends a lot on "stadiums"; if it's anything like my alma mater, MIT, it spends a lot on practical athletic facilities intended to keep its geek populace fit and relatively sociable.
2. Again, if it's like MIT, a huge portion of these royalties (at MIT, I think it was 30%) goes to the actual inventors. This is unlike private corporations, which typically give inventors a small cash bonus and 0% of royalties.
3. Swanky donor parties do happen; but to be clear, these are intended to raise money from donors, and are therefore effectively self-funding.
4. Can't argue with the president's house, but there is something to be said for having the president living right on campus. It's part of the pay package. Are college president's overpaid? Probably, just like US corporate executives in general. The argument is that you are competing for talent from some elite pool; you can buy into that story, or not.
5. You did not mention one of the most important uses for unrestricted funds, which is student financial aid. The group of elite universities that includes Caltech share a common policy of need-blind admission, and that no student will be unable to attend due to financial need. That money has to come from somewhere; and although there are targeted scholarship funds, those fall far short of the need gap.
6. Referring back to a previous point in the discussion, 40-50 years ago, universities made squat on their patents. But, on the other hand, the federal government was HUGELY generous with student financial aid, as well as other educational grants. As direct government sources have dried up, universities have had to fill the gaps from other sources, such as aggressive management of their patent portfolios. It's a bit sad, as this change in funding sources tends to work better for elite research universities rather than schools that are more focused solely on undergraduate education.