Even rarer is the choke done through sutemi waza, as was the specialty of Minoru Mochizuki's yoseikan budo aikido. See here at 3:00, 3:15 and 3:21--all chokes done from sutemi waza.
The choke is a powerful tool and it can be done altogether safely. All our chokes in yoseikan came from judo or from jujutsu and modified by judo's standards of safe practice. We never actually choked one another unconscious but stopped when the chokee tapped out. But choking was a fair option at any time in randori, for any attack that presented the opening. As you can see Washizu Sensei perform these techniques, they can be applied very fast and smoothly for devastating overall effect.
I know some groups practice chokes sometimes. I've done a little bit within formal aikido practice. It seems like an effective way to end an encounter and does not have to do any permanent damage to the attacker, so I don't see why they don't pop up more often.
I'm curious why there are so few choke techniques in aikido. Is it for philosophical reasons, practical reasons, or just a historical oddity?
Does anyone have any information or theories?