funding - Why do researchers need universities?

This is a follow-up question to How are junior professors evaluated for promotion? and probably an even more naive question. If I'm understanding the answer correct, professors need funding to do research, but once they get it, the university takes some of the grant as overheads (to pay for office space, electricity, etc), and the cut the university takes is substantial.

Given that then, why do professors need universities? One could just apply for the grant as per normal, and once one gets it, buy a slightly bigger house and convert one of the rooms into a lab. One loses nothing to overheads, gets to work from home, has zero teaching duties, can choose to settle anywhere (no two-body problem!), and can even monitor an experiment 24/7. This gets even easier if one works in a field that doesn't need a physical lab. Further, presumably the grant covers postdoc salaries, so one would still be able to pay for postdocs (although probably not PhD students since a professor without a university will not be able to award a degree).

The obvious answer is that one cannot apply for a grant without a university, but Google indicates that's not the case, e.g. NSA grants in mathematics only looks at one's previous accomplishments & potential applications of the research result, both of which are independent of the university. I suppose one could lose journal access, but there's always stuff like arXiv / ResearchGate, emailing the authors of the desired paper, or even Scihub (oops). It's conceivable that not working for a university loses one some prestige, since one can no longer claim to be a professor. However even then I'd expect at least some academics to choose this path, valuing the convenience & extra research funding over prestige.

If the answer to this varies from field to field, I'm most interested in the sciences.

Answer

If I'm understanding the answer correct, professors need funding to do research, but once they get it, the university takes some of the grant as overheads (to pay for office space, electricity, etc), and the cut the university takes is substantial

The number of services provided by a university is substantial, of which space and electricity are the least of them.

Maintenance, janitorial, and IT services - machines break, rooms get dirty, and technology has inexplicable problems. Universities have infrastructure in place to deal with all of this.

Access to literature - Universities maintain subscriptions to the journals, standards, and other references a researcher needs.

Laboratory equipment and specialists - Most scientific research requires specialized equipment, which can cost anywhere from a few hundred dollars to several million. Universities can afford to maintain such equipment, and the expert technicians needed to run the equipment at maximum efficiency.

Other researchers - A university department provides ready access to and familiarity with other experts in your field for potential collaboration. Additionally, it provides a way to find potential collaborators from other fields for the times when you find your research leaving the bounds of your expertise.

Students - an unfortunate amount of research is tedious. A university provides a ready framework for delegating simple but time-consuming work to students so that a researcher can focus on the parts of the research that only they can do.

Contacts - Universities maintain contacts with businesses, governments, and other research institutions that can open more doors than any one researcher could do on their own.

Reputation - Being a member of a respected university means that people who trust that university will afford some measure of that trust as well.

Legal services and other expertise - While it would be nice if research could exist completely separate from the outside world, this is not the case. Universities have systems set up to support and advise their researchers when problems arise during their research.

Many of these things could be aquired by a solo researcher, of course. But doing so would cost time and money, likely amounting to more than a university takes in overhead. And things like contacts and reputation are difficult to purchase.