Yes, Joseph, you're right about Alexandra - I'm not laughing at HER just the notion...(sorry!)
I feel a bit sorry for Ludwig I because, notwithstanding Gallery of Beauties, he had been a faithful & loving husband for many many years & had done a great deal to improve the lives of the people in Bavaria (including building public libraries etc.). It was only when he met Lola Montez that his life went into decline. He, an older man, making a fool of himself with some jumped-up little gold-digger...everyone could see it but himself. It was that which eventually led to his downfall. It's a shame. :-/