It's more about reach, which inevitably would slow you down. But i think he compensates through redundancy (i.e. many similar pieces of equipment spread over the kit).
I have a different question though: What's wrong with playing drums with your fingers? That's what the video seems to be about. It strikes me as weird to try to optimize away the use of the most expressive part of your body.
He is advocating a different technique that, based on his studies, would yield less injuries and more power, while still generating speen. He has been talking about this for several years now, about the importance of using the big muscles instead of the small muscles to generate speed.
Here is a short clip.
https://www.youtube.com/watch?v=FN3n-zmvJJABy setting world records on drum speed, and by retaining his drum speed even in his 50s, I think he is proving that his case is legit.
This made me think and ask the following question:
Would having the cymbals and cannon toms so high reduce his speed to hit? Not trying to criticize his playing or anything. Just wondering if lowering the upper hardware would increase speed and reduce the energy in his playing...In other words, could lowering the hardware be beneficial?
And just to clarify, I'm not trying to offend Mangini or anything like that...I'm not a drummer and do not play drums at all. This question just comes from a curious mind (and from an engineering point of view, since E=mgh).
Mike's cymbals arrangement is based on pitch, where they go R - L -R - L -R - L - R - L from the center going down the scale. As to why they seem so high, I think Mangini prioritizes spacing more, because having cymbals close to each other muddle the orchestration.
For the octobans, it's a combo of many things, practical, musical and aesthetic. From Mike himself:
"Firstly they’re in the middle for the same reason as my signature snares because I need to access them with either hand. I can’t have them stuck way to the left because sometimes my other hand is tied up. I just need them in the center for access. Another reason, which would make the most sense and be the most simple for anybody to understand even if they’re not a drummer, is there’s no other place to put them. Finally, they look like exhaust pipes up there. It’s just a good, fun look. I think that’s a great way to conclude the whole basis of my setup beyond the musical purpose of it. Me being who and what I’m making myself to be, and being happy to play, and all that. It’s fun. Drums are fun. Setting them up is fun. Hitting stuff is fun. I don’t know a better way for it to hit home than to say “putting those octobans way up high in the middle was a lot of fun”. I think that’s a good explanation."