The allegations against GT were related to NCAA amateurism rules and Institutional Controls rules. In my opinion, the NCAA was extremely aggressive in the investigation and punishment in that case. However, it was about actual NCAA rules.
My big concern about the NCAA getting involved in criminal matters is that the NCAA does not have enough investigative or enforcement power to handle such matters. Some sports fans appear to believe that being investigated by the FBI is nothing when compared to being investigated by the NCAA. Would you want the NCAA to investigate if an NCAA coach shot and killed half the football team to see if they should shut down the football program instead of the police investigating and putting that coach in jail? It seems to me that too often sports fans conflate the purpose, jurisdiction, and power of the NCAA. NCAA violations are often referred to as "illegal" even though no criminal laws are broken only the rules of a private(as in non-government) organization. It seems that many times people do not understand that the NCAA is not a law enforcement organization. From the "Core Purpose" of the NCAA:
They do use the word "safe", but it is in the context of competition being "fair, safe, equitable, and sportsmanlike". That core purpose is what the NCAA is set up for and what they are supposed to have rules and enforcement for. I don't think the rules or enforcement are extremely effective nor are they enforced evenly. However, that is what they are for and what they should limit themselves to.
If an NCAA investigator were to walk upon a rape or a child molestation in progress, he/she as a person should definitely try to stop the perp and assist the victim. That investigator and the NCAA leadership should report that situation to the proper authorities. They should also ensure that the proper authorities are taking action and report it to higher authorities if no action is being taken. However, the NCAA should not take it upon itself to be the investigative and enforcement body for criminal activity unless that criminal activity also violated actual NCAA rules. Even then they should stay out of the way of the proper legal authorities until they have completed their investigations/prosecutions.