Been there done that. I was briefly playing in a cover band that seemed to gravitate to the worst song every band did. For example, Queen "Tie Your Mother Down." I know for a fact that Queen has produced 20 better than songs than that, which everyone would know (and that don't rhyme with Bohemian Rhapsody). But OK. I went with it.
Cover bands don't necessarily have to sink to the lowest common denominator but most do. I didn't last long with those guys for other reasons (my choice to leave after two weeks). Conversely, my current band is 75% original. One of our covers is "Knockin' On Heaven's Door," which I normally despise because most classic rock bands just flog it badly. But we do a nice version of it.
If it ain't your band, you don't get much say. That's my experience anyway.