Gonna get briefer and briefer ... if you've read this far, you know the method, if what I'm claiming doesn't sound right, check Acclaimed Music.
The Beach Boys: Sixties icons. Best album, Pet Sounds, is #2 on the all-time album list at Acclaimed Music. By the early 70s, their prime had clearly passed. Brian Wilson, the guiding light behind the band, was 24 when the band made Pet Sounds.
The Beatles: This one is easy. The consensus pick for greatest band ever. When they broke up, the oldest guy in the band (Ringo) was 30 years old. Despite many great albums, none of the group's solo efforts ever topped what they'd done as Beatles.
The Drifters: Defeated the "theory" a bit by a nice bit of trickery, in that they changed most of the members of the group in mid-career. Whatever ... their peak lasted until 1964, at which time their lead singer of the moment, Johnny Moore, was 30 years old.
Bob Dylan: Because Dylan's had a resurgence (Time Out of Mind and Love and Theft were released when he was 56 and 60 years old), because he's had previous "comebacks," most notably in the mid-70s, because he still matters so much in his 60s, for all of these reasons and more, Bob Dylan is often mentioned to me as a guy who "proves" me wrong. But in fact, he's the boilerplate for my theory: early peak followed by gradual decline, with occasional resurfacing. Bob Dylan's first nine albums were all fine-to-classic, influential, timeless, the best that literate rock and roll has to offer. By the time he recorded Nashville Skyline, he was 28 years old. Bob Dylan was at his peak in his 20s. He then made some complete crap (I'm sorry, revisionists who try to rescue Self Portrait are deaf) and some average-at-best albums, then revived himself in the mid-70s, especially with Blood on the Tracks, made when he was 34. The 25 years after Desire were mostly of little interest, although occasionally he'd put out an album that was as good as New Morning. As noted, he's made a couple of excellent albums in the last few years. That does not constitute the peak of his career, which was clearly the 60s, not when he was 60.
The Supremes: Part of your opinion here will rest on what you think of Diana Ross's solo career. The Supremes are not my favorite Motown act, and Diana Ross mostly leaves me cold. In any event, the Supremes peak was in the 60s, Ross left the group when she was in her mid-20s, and after "Upside Down" and "I'm Coming Out" when she was 36, Ross made precious little good music.
That's five more artists, four of whom clearly fit the "early peak, then decline" pattern, one of whom, Bob Dylan, also fits but admittedly retains the ability to make great music into his 60s. I'm up to, what, 30 Hall of Famers, and I still see no evidence that rock and rollers get better decade after decade.