According to the LA Times, on April 18, 1971. the World's Best Rock Band is the Grateful Dead. I agree. For example, listen to Pigpen and the boys play Princeton University on the night before here
The Grateful Dead’s invasion of Dillon on April 17, 1971 — Hell’s Angels motorcycle gang in tow — is famous among devotees for a quintessential performance of “Good Lovin’ ” by band member Ron “Pigpen” McKernan, then suffering from what would be fatal cirrhosis. “The concert was expensive, $10,000,” says Lockwood, a faithful Deadhead who treasures a cassette recording he made that night.
The band played until “well past midnight,” Lockwood recalls, and “a substantial part of the audience, which was all students, was stoned out of their minds.” Concertgoers passed marijuana joints down the rows of seats, he says. According to legend, when a Princeton proctor demanded that shaggy singer Jerry Garcia extinguish his joint, Garcia snarled, “I’ll never play here again.” He never did. https://paw.princeton.edu/article/play-song-me