What will you do with your national anthem when you no longer have a queen? Singing "God Save the Queen" to a king would be kind of funny, wouldn't it?

Well it's not that hard. When there's a king they sing God Save the King, and when it's a queen, it's God save the King. Which does have the virtue of simplicity. If it turned republic they could sing God Save the President, though it'd be a mouthful getting through the last line, with the extra syllables. I suppose that's why the Americans didn't use it, since they are clearly fond of the tune, what with My Country Tis of Thee.

Or if my suggestion of Yellow Submarine was considewred too radical, the compromise could be to sing God Save the Submarine...God Save the Sub.

But as for "why are you still worshipping a position that doesn't really have any power" - technically speaking if you're praying for someone you can't possibly be worshipping them, it's a logical contradiction.