You are missing (or avoiding) the point. Musicians play music. Who wrote it does not matter. I want to play the best music, with the best musicians, in front of the most people, as often as possible. Who wrote it does not matter - again, as with someone playing Beethoven, Lennon, Rogers and Hart, Geddy Lee - whoever.
Who wrote it does matter to some musicians. Otherwise Rush would not have moved beyond playing Zeppelin covers.
BTW, it's "Rodgers."
Even established original artists like doing covers. Bob Dylan's new album is old standards written by others. ... I'd be hard pressed to think of any "original" artist/band that didn't do covers at times. I bet Beethoven did some Wolfgang tunes during his pub gigs.
Of course I agree. (But personally I have no interest in hearing "Dylan Does Sinatra." I'll wait for his next original album.)