I've been in very few bands that didn't play at least one original song. That includes the cover bands. If I get a vote in a band, I'll judge the song not who wrote it.
Labels are a pointless distraction, unfortunately, too many originals bands aren't original at all. The better bands (of any style) play songs that are interesting.
IMO a good covers band beats a bad originals band every time, and vice versa.