Eh, I don't agree with your lineage at all. I think the hypothetical "greatest band in the world" title has switched hands a lot more than 3 times.

Sure, The Beatles had it first throughout the 1960's. From there, I think the title was shared by The Rolling Stones and Led Zeppelin in the early 1970's. By the mid 1970's, it had passed on to Pink Floyd. In the early 1980's, it briefly passed on to AC/DC after Back in Black's release. Metallica had it in the mid to late 80's.

The 90's are a bit trickier. Nirvana (and the grunge movement as a whole) had a flash in the pan moment in the early 90's, but then they vanished for good right after that. This may be an unpopular opinion, but I'd consider U2 to be the greatest band in the world in the early 90's, not Nirvana. They were at the peak of their critical and commercial success after the release of Achtung Baby in 1991. The title passed on to Oasis from the mid to late 90's.

There weren't a whole lot of "big" rock bands in the 2000's. I'm a big Radiohead fan, but I don't think they can be considered "the greatest band in the world" during this time period. I believe that sort of title should belong to an act that had universal critical and commercial success, and Radiohead hasn't ever had monstrous mainstream popularity. For this decade, I'd say Coldplay and Foo Fighters shared the title throughout the decade. A few bands had a flash in the pan moment like Nirvana, but Coldplay and Foo Fighters were consistently popular.

So, my lineage would go:

The Beatles>The Rolling Stones/Led Zeppelin>Pink Floyd>AC/DC>Metallica>U2>Oasis>Coldplay/Foo Fighters

Again, I'm not judging "greatness" based solely on the band's quality of music. I'm basing it on their universal commercial appeal and their importance to the pop culture scene as well.