well, it's true that he may 'fight' a rider more than a fixed thing. but, to me, the reason you HAVE reins is to create a dialogue, which is taking and giving and engages some active thinking on both human and horse parts. I know you can use the idea of having a fixed thing against which the horse soon learns that fighting is useless, like hard tying , beyond that, I've never used nor been encourage to use ANY fixed training aid, like a standing martingale or a training fork. wait, I take that back, I did used a German martingale way back when I was first taking lessons.
the horse did not look all that comfortable, and I think while there was not a lot of tension in the reins, the bit was engaging. the horse will become really sore and tired if forced to carry it's head in a position it is not used to for a long time. If the neck is pulled up into an 'arch', which people think is so pretty, instead of just softly flexing at the poll, in time, it will develop large muscles around the third vertebrae. it may also develop a dip in front of the withers, if the horse drops the base of his neck down between his shoulders as a way to avoid the bit. it is, in effect, making the "S" shape of the horse's neck become tighter and more severely curved on both halves.
I think what should have been done is spend some time with the rider, getting HIM to sit better and learn how to 'talk' to the hrose through the reins. if the hrose 'fights', well, it means you aren't talking right.