There is lots of material on the subject. Do the research and decide for yourself. There is way too much information on the subject to get a quick summary from someone like myself or others, but the idea is good to gather up some of the evidence and information. I have literally researched the subject over probably 10 years and put in 100's of hours into it, (not just long toss, but other training including heavy/light balls) but unfortunately did not collate and collect all of my information to hand out, I just did it for my own knowledge to guide my son, which you are doing.
BTW the ASMI study has some fundamental flaws in their data collection which IMO (and some others) invalidates their conclusions. CADad who used to post here some time ago (who is actually a rocket scientist) pointed them out to AMSI and never received a response. It had to do with the Cosine errors in their velocity measurements. If you are that interested you could probably do some searches and find his comments here.
If it was my son at that age I would either get him into a Wolforth or Driveline program which included heavy/light ball throwing and integrate it with a long toss regime . BTW I would also have him do "long toss" from his knees for improved arm action, believe me this is huge for someone with poor arm action. They body is amazing on how it can adapt and fix something on its own without a bunch of "pitching lessons". I personally liked the concept of long toss as it was not "pitching specific" and it had an automatic feedback mechanism for the thrower. If he was throwing well then they can see it in the distance thrown. It got my son out on the field throwing baseballs, I know D'Oh but it is a way to get them more of this activity in, in a controlled and measurable way.
I have always been a huge believer in cross functional training as it has proven to improve athletic performance in the related event. I always go back to sprint training, as it is the most developed and studied of "speed related" athletics. They have a combination of under, over, specific, training, as well as weight training to improve speed performance. The weight training is very specific and phased also. You see these types of techniques being applied to pitching now and it does not surprise me that we are seeing the increased velocities of baseball pitchers across the board. Your argument that since pitchers only throw from the mound then they should only throw from the mound goes out the door if you look at it from the proven training done in other athletic endeavors.
I really like what Kyle is doing as he is studying it specifically for the throwing a baseball. Wolforth did it before him (and probably to a lesser scientific approach) and Dr John Bagonzi did it before anyone to my knowledge. (he got his PhD on throwing weighted baseballs and is the first to my knowledge to promote them) I got a copy of his thesis and don't know where I put it...
Of course with these velocity increases we will see a corresponding increase in injuries. As PG pointed out, high velocities induce higher loads, and since load is a squared function of velocity the stress levels are not linear we will continue to see higher injuries in pitching until some of the cross training techniques that Kyle is working on catch up.
So this is a long winded answer to long toss, yes or no, but in reality it should not just be the question of long toss but how do you develop an integrated plan for your son that includes long toss.
Best of luck to you and your boy!