I understand your viewpoint as well; unfortunately, bullies can also make use of MA against those they bully. If everyone takes MA, then the playing field remains basically level. Yes, good MA instructors teach the moral component as well as the physical; however, even in such cases, the moral component tends to lag behind the physical.I would like to see it mandatory in the school system. I believe it would help improve the bully situation by giving the victims better physical abilities and a confidence boost. I also think (or hope) that the bullies would gain a new insight in terms of respect for others. Unfortunately, I don't think it would ever materialize.
As both a teacher and a TKD instructor, I would love to see MA introduced into schools, possibly even as an activity for students who are being bullied - but having seen both bullies and bullied, I think the moral component would pass many of the bullies by, and having been a somewhat shy bookworm who did poorly in PE in school, I don't think I would have tried any MA if given the option, and would have done the minimum required (as I did with gymnastics when it came up in the PE curriculum) if it were mandatory. I chose to start TKD when I was 20, but much before that, I don't think it would have been effective - I would not have been ready to take it, nor would I have wanted to be forced into such an activity.
As far as a contrast to team sports goes, well, many of the same students who excel in team sports would excel in MAs, and for the same reasons - coordination, strength, etc. - and would still leave those who do not have those skills behind. Sure, some students would do better with MA than more traditional PE curricula, and some students who excel at team sports would do less well in MA than in team sports, but overall, I don't think it would change the status quo much.
Working, as I do, in a middle school with a wide range of incomes, religions, ethnicities (nearly 1/3 of the school qualifies as English Language Learners one way or another, and at last check there were 15 languages besides English represented among the students), I can also foresee parental objections based on religious concepts (anything from meditation to fighting, which many religions object to on principle), on the basis of gender (my daughter shouldn't have to learn to fight, my son shouldn't have to fight girls, etc.), and so on - all of which I have seen as a TKD instructor, and/or heard about when the occasional girl wants to join the wrestling team, or the occasional boy wants to join volleyball.
It's a great idea in concept - but in reality, I don't think it would work as part of the PE curriculum, unless you started the kids really young and kept it going through high school, and there aren't enough instructors for that. Starting any older and making it mandatory raises other problems. There are too many confounding factors.