It always amazes me how difficult some bands make the task of choosing songs. There are, literally, thousands of well-known songs to choose from that general audiences will happily enjoy, and as many again if you focus on a particular genre (e.g. ska, classic rock, country...)
Assuming that any band has a basic genre or style and that the band members don't actively dislike the music that fits the band, it shouldn't be hard to pull together a couple of dozen songs that everyone agrees on.
Both bands I'm in regularly share videos on what'sapp and rather than actively chucking songs out we tend to have songs that come up where we all say 'yes'. Yes, we have the usual constraints - the vocalist says he's been in a band singing Dio songs, and he doesn't want to do that to his vocal cords any more. The drummer likes things that stretch him. I don't like songs that just have root eighth notes.... But this positive discussion has brought in a lot of songs that are new to at least one or two of us. I have never thought of doing Audioslave or INXS before. We all have been pretty excited by the suggestion of a Manic Street Preachers song. Despite scepticism, we enjoyed doing a Tom Jones song (Sex Bomb) so much, we're going to rock up Delilah as well.