Uniform probability yields maximum uncertainty and therefore maximum entropy.
Jeff Atwood from Coding Horror thinks that the button is Google's number one UI mistake: "I understand this was a clever little joke in the early days of Google-- hey, look at us, we're a search engine that actually works! -- but is it really necessary to carry this clever little joke forward ten years and display it on the monitors of millions of web users every day? We get it already. Google is awesomely effective."
"You know Larry and Sergey had the view, and I certainly share it, that it's possible just to become too dry, too corporate, too much about making money. And you know what I think is really delightful about Google and about the "I'm Feeling Lucky," is that they remind you that the people here have personality and that they have interests and that there is real people," said Marissa Mayer.