Here's a brief look at some other band's interpretations of White Light / White Heat songs.
James Murphy of LCD Soundsystem is a demonstrated gigantic music fan. It is no suprise that he would have chosen to reference the Velvet Underground at some point. One example is "Drunk Girls" nodding to the "White Light / White Heat" call and response.
One the biggest fans of the Velvet Underground among their contemporaries was David Bowie. He regularly performed "I'm Waiting for the Man," and here he covers "White Light / White Heat."
I think Nirvana's take on "Here She Comes Now" is really great. I always like when a band can honor the original and also put their own stamp on the cover. That's the case here.
"Sister Ray" is not a song I imagine many being excited to cover since the original is so daunting and distinct, but the Joy Division did a pretty good job of it. Check out this version from 1980.
Any other covers you recommend? Any connections you've noticed?