There is no doubt that brain trauma and injury can accumulate over the years of fighting professionally, but when getting started in the sport nothing is full contact until deemed ready. The structure of the MMA gym I trained out of for four years was such that I required a certain amount of time working one on one with an instructor, establishing my basic techniques before I was allowed to go “live”, or spar. All the sparing I did at first was light, until I was comfortable transitioning to more heavy sparing sessions. No matter what I was doing though, I would be faced against opponents who were better than me, in a sense that they knew how and more importantly how not to injure me. As a general rule, the younger and the less mature the practitioner, the less full-contact is allowed, and most training facilities that are professionally run are organized in this manner.
One of the most important reasons however, for the lack of injury, is that an MMA athlete is trained to be offensive as well as defensive. Compare this to being unfairly tackled when trying to score in soccer game or accidentally falling off a horse when jumping a fixed obstacle during an equestrian race. One reason that injuries are relatively low in MMA stems from this, that MMA is a sport where you are prepared and trained for impact, not where your key task is something else and you might get injured in the process.