Well, if Iwere standing there, at absolute attention, not moving, probably praying to God that I didn't get the urge to sneeze, wipe my nose, scratch...well, never mind--after 20 minutes, I'd probably want to get relieved too.
My other guess is that there are a multitude of officers who either were assigned to this detail, or wanted to be so, and continually rotating them offers as many as possible to perform this noble service.
Just my $.02
After I posted that....I thought the same....what an honor..to be able to tell your children/grandchildren...."I stood as Honor Guard for President Reagan at his funeral"....it just slows the process so, as the line stops, is my other thought.