If the in-hand work you want to do is to develop passage/half-steps/piaffe, as opposed to the groundwork that Tristan Tucker does where he typically uses a rope halter, using a well-fitting cavesson is extremely important.
Amberley and belgianWBLuver’s comments about cavessons used while doing in-hand work are notable. There are people who give in-hand clinics to teach passage and piaffe who don’t use a cavesson, so there’s danger of hurting the horse’s mouth. I’ve watched YouTube videos w/ fairly well-known clinicians who teach piaffe/passage clinics, and it’s disturbing to see how the horses don’t follow the basic tenets of dressage - there’s no effort to keep them straight, rhythmic, and responding to half-halts. It’s disturbing to see horses rushing forward and/or circling around and having their mouths yanked. Basically they’re just holding the horse with the bridle and tapping their butts with the whip.
The SRS Bereiters I’ve taken in-hand lessons from always use a cavesson over the bridle, with sidereins, so that they can half-halt and control the horse without hurting the mouth. They emphasize that the pyramid of training applies while doing in-hand work just as it does while riding - the horse must be relaxed, rhythmic, straight.
The SRS cavessons are wonderful, and yes, agree that it’s hard to find anything like them in the US. I just finished a clinic with an SRS Bereiter, who brought over a cavesson for one of the regular riders. It’s pretty typical that people ask him at clinics to bring a cavesson back with him when he returns. I treasure mine. 
