Iconic songs of iconic performers should not be covered by others for a long time, but there is a time after which it is fine to do so. I am unclear about the time frame, and I think it is variable, depending on the performer of the original song, how intimately the song is related to that performer, and the status of the person covering it, and the nature of the arrangement of the cover.
Covering Sinatra's My way or New York, New York is fine now, but would have been risky in the 70's. covering a few Elvis songs, except as a tribute band, a few Beattles songs, maybe the Stones, the Who, or Floyd would all be dangerous until some substantial years have passed. That said, great music needs to live again, and covering it makes that happen. I was not concerned when Aretha Franklin covered Bridge Over Troubled Water. Dylan was not concerned when Hendrix covered All Along the Watchtower, nor when Dave mason or the Dead did so as well. I think George Harrison was happy with the Jeff Healy cover of While my guitar gently weeps. And lord knows, Clapton, Harrison, and Waters seem to like collaboration and covering each other's work.