In some ways, it is very strange to make an 88 year old great-grandmother visit sets of TV shows. Plus, she probably doesn't watch very much TV, since she's so busy visiting people all day, and if she does watch TV, it probably wouldn't be Game of Thrones. I will say I do not envy Queen Elizabeth II; it has to get tiring to do the same stuff over and over again.
And I guess Elizabeth disappointed everyone by not sitting on the throne. She's 88, for cripes sake, she doesn't want to sit on the sword throne! (I've never seen Game of Thrones, but my twin sister tells me it is DIVINE.)