A lot of the most memorable covers did something new and interesting with the song, not just tried to sing the original as close as possible with a new singer.
This sort of thing is one of the reasons that (for example) I greatly prefer the 4e Dragon Magazine version of the Against the Giants series to the Tales from the Yawning Portal version. The former cleaned up the original with more named NPCs, more variety to the encounters, added a whole location for the Stone Giants, improved the maps, and gave the DM more guidance on what the motivation was for the entire plot. The TFtYP one just updated the original to 5e, warts and all.
I would have loved the 4e one updated to 5e, with some thought given to improving it another step. But c'est la vie.