It is a question of overhead.
What percentage of tuition goes directly to teaching students and direct support staff, and what percentage goes to other things.
What percentage of the budget is consumed by research and programs not related to teaching?
Your questions appear to be based on a misconception of the purpose of an university. Universities engage in research, teaching and service, Different universities have different missions, so the relative effort in each category will be different.
Typically research is not funded through tuition though. Grants for research come from government, charitable, and corporate entities, and they typically require strict accounting to show that the money so granted doesn't get diverted to other purposes (teaching, maintenance, etc.) outside the terms of the grant.
One of my first jobs was with a UK company called Hyperdata (now defunct) whose entire business was the provision of computer accounting systems specifically designed for university departments. Back in the late '80s, it was such a niche market that we usually had to supply hardware as well as software, as the accountant's standard 286 machines weren't capable of running our core application, which needed a 386 processor and minimum 4MB of HDD storage.
Tuition was completely isolated from research grants back then by a small army of dedicated bean-counters; I suspect that the army is much smaller and more efficient today, but certainly no less effective in financial ring-fencing of the various activities.
Of course, things may be very different in the US, but I rather doubt that your grant issuing bodies are any more relaxed about the potential for their cash to be diverted to purposes other than their intended ones.