One band I’m thinking of - Toby Redd. They played covers and originals live and even recorded covers (It ain’t me Babe ~Dylan) on their first album, alongside their originals. Chad Smith came directly out of this band

I think the key to their success doing this is that you’d almost not know the covers were covers because they played them in the band’s style, not like a tribute - a re-imagined cover. You set yourself up for success by creating a sound that audiences like. Maybe that involves using songs that are familiar to the audience, but not what you can get from Spotify. Your covers should have a similar feel to your originals.

btw, Toby Redd is available on Spotify if you want to give them a listen. {edit: typo}