Cover songs may have a worse reputation than they deserve: Sometimes, they're considered lazy grifts by musicians less talented than the original artist. Or they fail to come anywhere close to the original's quality.
And we've certainly heard our fair share of great songs getting abysmally butchered in cover versions. Leonard Cohen's Hallelujah is a prime candidate for bad takes. It's probably human to distinctly remember the negatives.
However, cover versions used to be much more popular and less frowned upon in the past. It was even more likely that a cover song surpassed the original, and today, many people wouldn't even recognize that it's a cover. Jimi Hendrix's cover of Dylan's All Along the Watchtower is one of the most famous examples, but also Aretha Franklin's Respect, originally by Otis Redding, or Ike & Tina Turner's take on CCR's Proud Mary.