There are lots of “devices” that are legal in one division, but not another.
Dropped (or flash, or figure 8)nosebands, standing martingales, gags, twisted bits, double bridles, bimetallic bits, elavator bits, long (dressage) whips, ear plugs, bandages, etc.
Every one of these (though I have my doubts about the twisted bits)has a legitimate training use. None the less, they are illegal in one or more disciplines. Why? I think it has more to do with history and politics than anything rational.
(For example, the objectives of Dressage, and the dressage phase of a Horse Trial, are very similar, but there are SIGNIFICANT differences in the permitted equipment. Why on earth should a dressage whip be legal for a dressage class, but not for a dressage test at a horse trial?)
Anybody trying to find a RATIONAL reason for any of these things is propably just wasting their time.