It’s really hard to do a faithful cover of an older song, and by older we mean something from a previous era.
There are lots of attempts. Laura Nyro did a tremendous cover of Jimmy Mack (having LaBelle back her up didn’t hurt). Bob Dylan wrote All Along The Watchtower but even he said that Jimi Hendrix had the definitive version.
But those were more or less contemporaries.
The Rollling Stones covered a lot of earlier American songs like Chuck Barry’s Carol and Willie Dixon’s Little Red Rooster. They got better at it but the early Stones were basically an average cover band.