I've never played in an originals band but write and record my own stuff at home which virtually no one listens to. I mostly find that I don't push my abilities that much when writing my own stuff. Playing covers forced me to learn to play things that were difficult sometimes and made me a better player.
I didn't really enjoy gigging that much - it was a necessary evil of being in a covers band but I enjoyed being in a room with other people just to make music - whether it was someone else's or not was irrelevant, and the reaction of an audience to a song they know is satisfying.
The hardest thing about being in a covers band is getting everyone to agree what covers you're going to play, or having to play songs that you simply don't like while pretending that you do.
I struggled with the idea of being a musician while not actually creating anything of my own but overcame that very quickly. The vast majority of musicians though history have played other peoples compositions whether that be orchestral, jazz standards, traditional folk songs or whatever.