When I listed bad habits that drive me mental, I forgot "the leader moving the follower around using the arms." That pretty much guarantees back and shoulder pain. Ugh.
My partner and I are always changing what we're working on, meaning that our exercises at the práctica change, too. However, one exercise we do every single time is dance at least one tanda arms-free. The only point of contact allowed is the torso. Every major family of tango movements other than colgadas, including overturned movements, can be danced this way. At this stage, we use milonga tandas for this, because with short, sharp movements at high speed, there's no room for error – either it works or it doesn't.
I believe that all tango should be this at its heart, with the arms added strictly for a bit of extra safety – like a seatbelt, something you put around you but hope never to need. Colgadas aside, any movement a person can't dance without implicating the arms is one they need more work on. An absolute need for arms is a sign that they're not really transmitting and receiving with the core.