I let my daughter do martial arts, so why not, provided they have proper safety equipment. It would also depend upon their teaching methods and what and how they teach. The martial arts school she went to didn't just teach the physical arts, it taught mental discipline, respect and honorable code of conduct. If this was not included with the boxing lessons then I probably would not allow her to go to that school but send her to one that does.
They seem to have changed a lot of the old practices in recent years now that they have learned more about the dangers of concussion at such a young age.
I don't think that I would stop a child of mine from learning the sport if s/he wanted to.
