Why do researchers need universities?

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.

Another point is about the social environment. Research is a process with many needs, and one of them is contact with like-minded people to share insights, problems, day-to-day peer review, and so on. The lab is not only where the researcher does physical work, but a place where other researchers, students, and whole communities meet to have social exchanges. The university does this at a much larger scale. Even hard sciences like STEM need this social aspect.

The lone and autonomous scientist is a romantic view. Some papers on fringe areas have more than a hundred co-authors today.

There are really two questions here. 1.Do researchers need support? and 2. Do researchers need support from an organization that also teaches?

The answer to the first question is: As arrogant as some researchers are, they need support, from any number of other people. From human resources, to accounting to janitorial. If any researcher honestly thinks they are capable of doing all of those things better than professionals they are either laughably naive or simply stupid. If those researchers think they don't need those things and believe they can work in a vacuum, the same statement applies.

The answer to the second question is a bit more complicated but comes down to a couple of ideas, on the concept of giving back. Those researchers learned somewhere, most often a university and want that system to continue because they recognize the value even if it does "cost" them some percentage of their funding. The other is that most people recognize the value of new ideas and having to explain yourself to those with less knowledge than oneself. Universities also provide for continuity of research, very few projects are one and done, the environment of constantly changing students provides a way for ideas to grow and evolve or be supplanted by better ideas.

Finally from a funding perspective, funding entities recognize the value that universities provide to researchers and society as a whole and probably include that in their calculation when choosing what projects to fund.