Ancient India has several instances where the next ruler was selected by the royal elephant. Of course, it was not meant to be random, as the elephant would pick a righteous person capable of steering the kingdom at that time.
NoTA does not solve any problem. It just gives one more avenue for the parties to play with. E.g., parties will try to push voters of their opponents towards NotA. Also it leads to worse outcomes as dreamers/perfectionists choose NotA instead of voting for the best option available, while hardcore supporters go and vote for their favorite candidate.