After getting the crap beaten out of me all morning, I am happy that you agree that our heads of state are not in any way inferior to the the Queen. But I would also like to say that our Founding Fathers went further than that and stated that all of us are created equal - that is, equal to anyone who considers him/heself royal - and have been endowed by our Creator with certain inalienable rights - that is, rights not bestowed at the whim of a sovereign who could just as easily take them away.
I told you already - the Queen couldn't take a lollipop from a baby, let alone anybody's rights.
The British royals haven't had any power to speak of since well before the days of Queen Victoria. She tried to exercise her right to choose her own Ladies of the Wardrobe, and all hell broke loose. In fact, I think you have to go back to before the 1688 Revolution to find any English king who subscribed to the sort of Divine Right thinking in Eikon Basilike. (And a lot of good it did Charles I, anyhow.)
You are attacking a straw man of British sovereignty that hasn't been around for at least 300 years.