I do not have any research to offer but a few personal observations:
I recently had a good number of new clients all of whom told me that they had been doing HIIT training or kickboxing. What they had in common was that they did not get that sense of well-being which should be the result of exercise. Instead they had aches and pains and were wondering whether this was the best form of exercise for them.
The results of my assessments were that they lacked the structural stability necessary for this high-intensity form of exercise.
That does not mean that HIIT training and kickboxing are inherently dangerous if done by a person whose body is ready for them. I have my doubts, though, whether a proper assessment is made before people are admitted into the classes.