I agree that the remaining Beatles would have been successful in their own right, without Paul McCartney.
We also must look at the evolution of Top 40 radio in the fifties. There were no personal music players and many home record players wre of poor enough quality that AM radio was a viable source of music. Top 40 was not the nationwide countdown program initiated by Casey Kasem in 1970. Publications like Billboard and Cash Box did publish surveys, but they would not have been suitable for a radio countdown in the fifties because a given song often appeared several times, by different artists, in a given week.
Surveys had to be local. The first was conducted by broadcaster Todd Storz as he polled record stores in Kansas City in 1954, combined the results with logged listener requests, and published a Top 40 survey. The record stores cooperated because the surveys were a useful marketing tool. The theory was to rank the best selling songs from, regardless of content or genre, and play them in a 40 to 1 countdown each week. The process would generally bias towards anything new or innovative, especially rock and roll. Top 40 would spread rapidly in the late fifties.
Elvis Presley placed 28 songs on the Billboard Top 40 between 1956 and 1958. That is a lot of space to fill. More significantly, Elvis took rock and roll across a racial divide at a time of discrimination and segregation both on stage and on the radio. Would Bill Haley and Buddy Holly be able to do the job? The baby boom would foster the growth of youth-oriented music. How would it change without Elvis at the helm?
I would assume we would see a slower, more subduded progression for rock and roll. You might butterfly away the payola scandal, where disk jockeys were illegally bribed by distributors to play certain records. In turn, you butterfly away the conservative backlash against rock and roll, where the music was branded as evil, immoral, work of the devil, etc. In OTL, music slowed down in the US from 1960-62 as the cutting edge of rock and roll migrated to England. In ATL, you slow down music in the late fifties but keep a steady pace into the sixties.
By the mid sixties, music will be subject to the same pressures of OTL: a burgeoning young baby-boom audience, rapidly improving high fidelity technology and a demand for recordings that fill the entire audio spectrum. If the Kinks can come out with anything like "You Really Got Me," the time line will heal very fast.
Bob Dylan did not put songs on the chart until 1965. Artists like Dylan and the Beach Boys would emerge relatively unchanged, or different only in as much music in general is different. We should also remember that in the mid and late sixties, fifties rock was no longer popular.