Listen, if you can't see the benefit of it, don't do it.
I can see the training benefit of HR monitors on training runs (or power meters for cycling), although I don't use them. I can see the training benefit of pace information from a watch, although I don't use a Garmin. But it isn't confusing to me how someone would find that useful.
As for breathing rate, this isn't a matter of "monitoring" If that is how you think of it I am not surprised it seems like such a big distraction to you. It is just being aware. Do you "monitor" your level of quad pain during a race? No. Are you aware of it? Probably.
There is all sorts of data available to you from your body. Pain, fatigue, breathing rate, etc. You can use or ignore this as much as you like. One of the many things I would notice 10 miles into a marathon would be my breathing. I don't think anyone here is talking about counting steps per breath in a championship 800. Can you get this?