I had a very similar experience myself. Andrew Reese was one of the top TPE QBs in the league toward the end of his career, but he never stood out. Even from a player standpoint, it was infuriating simply because I was busting my butt just to be mediocre. I do feel that QB is based partially on your own TPE and partially on the stats/TPE of the players around you. Good receivers can elevate a QB that looks weaker on paper and you almost need the combination of both for a QB to thrive consistently. And, of course, the pressure of being both a GM and a QB is awful. I do not recommend that for anyone. It's no coincidence that my next character was a complete meme designed to entertain myself; the burnout from playing QB took its toll and my soul needed cleansing.
This said, I do think it should remain a player position. Regardless of how infuriating and demanding the role is at times, with the right mix of hard work, planning, and luck, you can be an absolute star and the chance at the spotlight that comes with that will attract players. Not everyone will have a positive experience as a QB, but many will still try their luck. I like the approach that TC and Opera both mentioned. There are so much variables involved that are out of your control that you can't take failure to heart. If you're doing the work, you just have remind yourself that you've done everything you can and hope for the best.
This said, I do think it should remain a player position. Regardless of how infuriating and demanding the role is at times, with the right mix of hard work, planning, and luck, you can be an absolute star and the chance at the spotlight that comes with that will attract players. Not everyone will have a positive experience as a QB, but many will still try their luck. I like the approach that TC and Opera both mentioned. There are so much variables involved that are out of your control that you can't take failure to heart. If you're doing the work, you just have remind yourself that you've done everything you can and hope for the best.