It should be noted that the 'staying out of politics' is a public phenomenon. In her weekly meeting with the Prime Minister, The Queen makes her political stance well known (that is the entire point of the meeting).
Frankly I would rather have this lobbying out in the open where it can be held accountable.
She is also the only person in the world who has the experience of a weekly conversation with the last 14 prime ministers of Britain. She is the embodiment of the state’s institutional memory.
While the office may have had consecutive local minima, one would be hard pushed to suggest Major, Blair or even Brown - were "downhill" from Callaghan.