My experience is that Gleason Sensei's dojo sets an unusually high standard for weapons work. That may or may not have anything to do with their use of tsubas, except that I would be extremely reluctant to face Gleason Sensei without one.
The example you provided in the post above this one is an example of where the tsuba is clearly required by the technique.
But I am curious why you say you would be reluctant to train with Gleason Sensei without a tsuba. Do you think he would hurt your hands accidentally or intentionally? Or would you be worried that you would accidentally hurt your own hands? Or are you simply pointing out that Gleason Sensei does a lot of techniques that require a tsuba?
I apologize if my line of questioning seems overly aggressive. Sincerely trying to figure something out.