So what exactly does the reiho teach? I don't think a lack of reiho means there is a lack of sincerity, or that you treat people poorly, or that you don't respect others.
On the other hand, are most checkout clerks sincerely happy that you shopped with them today, or do they say that because that is what is expected or required?
I think reiho is actually crucial to a certain type of pedagogy where the student learns intuitively as opposed to analytically. This is probably more important than keeping calm and order in the dojo.
One thing I have noticed when engaged in kata-based training is that I will screw something up and then, rather than stopping, and fretting, analyzing, or asking for a do-over, I will simply proceed with the kata. I will complete the whole thing and move onto the next one if that is what I am supposed to do. I still analyze my mistake but that happens off-line, after the training session is over.
I can't tell you whether this is good or bad but I can say that training this way tends towards much higher mental intensity levels, and my offline analysis seems to lead to better insights than if I were to fudge around in the middle of practicing a technique.
It may be that reiho is not the only vehicle by which to inculcate this kind of training mentality but it seems to do it for me. It works to prevent people from standing around on the mat talking about training, and encourages them to train instead.