I find it amusing. The folks who are "teaching" this -UTD- seem to think it's new idea. It is how diving use to be done until the BC came along. All the vintage divers I know dive this way. We don't use side mount but otherwise it's the same. We use either a packplate and harness or a simple tank harness. As long as you are not wearing a lot of wetsuit it actually very easy to dive this way assuming that you are perfectly weighted. Weighting and buoyancy control become critical but done correctly it's a very enjoyable way to dive. Most divers do not have their weighting or skill level to the point they can easily dive this way, they are reliant on their BC to make up for poor weighting and buoyancy control. I am not saying it's best for all situations, far from it. When diving with a dry suit or in a thick wetsuit a BC makes life a lot easier but with little wet suit in warm water it's my prefered way to dive. If you want to give it a try but have a backup plan, try this. Get your weighting to what you think is correct..which IMO is dead on neutral at 1/2 tank pressure...then go dive your normal BC but at the beginning of the dive dump ALL of the air out of it, make sure it's stripped clean of air and do not add any air until you surface. I use 1/2 lb weights when I weight for no BC diving, I want it that close. It will not give you the freedom you feel with no BC but it will let you get a handle on proper weighting and buoyancy control. Once you can do that comfortably find an old BP and dive a pool or other safe confined water until you get the hang of BC less diving.
I recently spent a week on Bonaire diving with no BC, I got ask a lot of questions but no one objected. I am sure a lot of dive ops will not let you dive this way and I have on occasion "overheard" instructors saying (I know they intended me to hear) that diving that way is unsafe. I usually find their class and hang around for a few minutes showing the class what buoyancy control really looks like.
BCless diving is not new, it's old school and a really enjoyable way to dive....I do agree that the side mount tank looks a bit unconfortable.