I guess you need to compare universities to research institutes like Howard Hughes (HHMI). Unfortunately only academic institutions are eligible for grants from NIH/NSF, so they don't break down their costs like that.

Most non-university non-industry non-government research institutes in the US (eg. Salk Institute, J. Craig Venter Institute, Sanford Burnham Prebys) rely on their researchers applying and getting grants from the NIH and NSF just as university scientists do. And their overhead costs are generally even higher than universities because they have no other source of income other than grants (I used to be faculty at JCVI). HHMI is unusual in that it is funded by a rich person's estate and doesn't need this.

And HHMI makes lease payments, etc, on facilities for researchers at partner institutions that cover a lot of what would be incorporated in indirect costs.

They also cover expenses of people, not specific projects, so the broader grant means that there's less of a need for common overhead across projects.

This is incorrect: while some NIH and NSF grants require an academic institution as the prime or sole awardee there are many that are open to private organizations and others that are mandated to be specific to small businesses (SBIR).

Research funding awarded to universities and to performers internal to NASA (back when there was a reasonable amount of that) had overhead rates that were similar to the NIH rates. When I worked at Xerox PARC, we would perform research for other parts of the company and charged overhead too, although the rate was a little lower (around 40%). Institutional overhead has been a regular feature of how research has been organized and funded for 60 years. Change is fine, but most of the costs are legitimate, and it takes time for the rest of the system to adjust to changes in one part of it. Doing it abruptly is damaging the system and will negatively impact the careers of many students and young researchers.