And here starts the debate between musician and artist. Musicians aren't certainly required to create anything new. You can be a completely competent musician, maybe play in a cover band, do things exactly as they're recorded, in time and with feeling. That's a great musician. But that is different from being an artist. An artist creates something new. Or at least something new in their head even if it isn't re-inventing any wheels.
I think you're selling yourself short if you're trying to live up to some kind of "perfect musician" in your head. As long as you're happy making music.... even if it's not your own, that's good enough in my book to be a great musician.
Which is why I place live music above all other art forms. As an aural form, music truly exists only in the moment of creation, is witnessed only by those in earshot, then is gone forever. Be it the Berlin Philharmonic playing Mozart, any Glastonbury headliner, a cover band filling the floor at bar, a bloke with a guitar busking in the street or whatever, great live music has an immediacy and intimacy like nothing else. It demands attention - blink and you miss it. And anyone part of creating that is, without doubt, IMHO, a musician.
You guys have clearly never heard me play in a live setting. Even when my hearing was ok and I was playing a fretted bass with the notes at least in tune.....
Playing covers never gave me any trouble; I do ok and do enjoy some cover playing, but that wasn't what I wanted to keep doing going forward. But the irresistible force of wanting to be a musician/artist finally met the immovable object of you just don't have those instinctive, creative abilities to do that. And plus you're going deef standing right next to that drum kit all the time. I kept it up for some time, and finally decided after many years of hard effort with no progress that it just wasn't going to work. I haven't played in a group since, though I still enjoy playing as a hobbiest and as a gear nut and so on. I might even end up collecting perhaps, or relearning repair or go into luthiering, etc.
Jeff Berlin talks a lot about a similar division, his concepts of "academic music" vs art, and the importance he places on keeping those two separated properly. I have done searches here on JB, though, and seems like there was a lot of fighting about his approach to music, so I won't go into anything about that here at the risk of dredging up another battle over JB's approach. Except to say that I also recognize the differences between what I call the "craft" and the "art". One being the tools you use and the other the artistic output from putting the tools to use artistically.
Otherwise, the OP asked an honest question and that's my honest answer, as best as I can render it....
L