Forget the power hungry psychopath thing for a minute. What the Queen said is interesting. It reminds me of what former US presidents said about the presidency. Cleveland said to a 5 yo FDR "I hope you'll never be president". You also never see former British PMs or US presidents say they miss the job.

There's a recurring theme here. Why are these positions so undesirable to those who occupy them? What's the common thread? Personally I think it's a combination of the weight of the responsibilities carried by the office, and the fact that being a leader in a democracy is inherently undesirable. You can't do unpopular things, you have to face constant criticism, you can't speak freely or you could offend sonebody. Smart people, for the most part, are repelled by a career in politics.