Double lip embouchure is the way the clarinet was played when it was invented in the 1700s. It was also common to play with the mouthpiece rotated so the reed was on top, for which a single lip embouchure is impossible. Playing with the reed on top was mostly abandoned in the 1800s, although some Italian players continued doing it until the early 1900s. Also in the 1800s, the German player Klose advocated using a single lip embouchure instead of double lip, and most players worldwide gradually switched to it. A summary of the history can be found here:
https://clarinetcorner.wordpress.com/2013/05/05/mouthpiece-puzzle/Some classical players still use double lip, and you can find videos online advocating it- for example, the maker Tom Ridenour likes it and refers to it as French embouchure.
I don't know what proportion of jazz players use double lip. I do use it myself and find single lip awkward.