It's not a question of "holiness" but of decorum-- a sense of order and fittingness and a time and a place for everything. It's something the office of the monarchy and other institutions like the military, etc., are built upon, even since the early years of our Republic. That's why we salute the flag and treat it with respect, for example. It's something we've lost a sense of and our culture is the poorer for it.
Yes, but, some of that ‘decorum’ is BS.
That no one can touch the monarch is similar to no one can enter GOD’s presence (which is absolute truth), only stupider and thousands of order of magnitude more wrong.