I don't think the queen is smart enough to make plans such as abdicating as suggested above to bring charles in to sort things out and streamline the monarchy, and that's not just because of her age. (Not that I think that would be a good move anyway.)
She's been praised over the years for being a great monarch but for what? She just hasn't had direct scandal for anything she's done, basically stayed quiet and done all the constitutional things expected of her. That doesn't mean she's 'great' or that no one else could have done as good a job. I think she's made up her mind not to abdicate and that's that. She's not such a sharp thinker and is pretty set in her ways.
Her judgement, and that of her kids and grandkids, has been terrible at times. The royal family PR is usually one step behind the curve, unless, in this latest case, some staff hate andrew so much they let, or even encouraged, him to do this interview so that he'd hang himself.
The queen doesn't seem to like change. She didn't like lowering the flag for Diana when she died as it wasn't done in those circumstances. It was only when forced due to public opinion and strong advice from staff that she did it. She also didn't like having to bend to the public's will that someone needs to say something about Diana's death, as far as I recall. I felt when this happened there was definitely an air of some crisis going on with the public and the royal family and it was a wake up call for the royal family that no, they could no longer do exactly what they pleased and the public would respect them regardless - and I don't think they liked it, including the queen.
She's as entitled as the rest of them and while I don't find her unlikeable (or particularly likeable either) what she stands for is and some things she does too - the medals, titles, houses etc awarded to her kids as if they're something special beyond the position they have beyond it being an accident of birth. When her mother was alive the press fed us the line about "the nation's granny" and wasn't she wonderful etc. No, she wasn't as far as I could see. We were brainwashed for years about this family and now the mood is changing and the royal family don't like it and are so arrogant they're dumbfounded that we don't want to doff our caps to them anymore.