So the stone in theory, goes from being the pillow of the father of the 12 tribes from which he drempt of heaven and angels when he rested his head on it....to an object so revered that the Celts wouldn't dare even touch it...to placed under the ass of the British monarch when he or she is crowned. To add to that, their feet are on a representation of the earth. God's creation. By putting their feet there they are claiming dominion of the earth and all therein.
Look up Bible references regarding these things I have pointed out. If nothing else to sit on a stone that has biblical myth attached to it shows immense disrespect in my opinion. To stand on a representation of God's creation as you are "crowned" a king of earthly realms is also disrespectful in my opinion. It shows who thinks they are king...not so fast, chuck.
Just my personal musings...