Carpenter is not a middle of the pack #2 or #3 starter. A middle of the pack #2 or #3 starter would be somewhere in the range of Gil Meche back before he got hurt, or the Andy Pettitte of 2-3 years ago. Carp's had his injuries, but when healthy he's a #1 starter.
Besides, you're wrong. There's nothing about being a starter that would magically make you more effective in the bullpen. Starting is about a good arsenal of secondary pitches and good platoon matchups against both sides of the plate. If you have that , you can get through the lineup more times without losing all effectiveness. That doesn't mean that you always dominate the first time through like relievers have to. That's also a question about arsenal, just a different one, one that depends more on one to two really good pitches than on the deeper arsenal of most SP's.
There's obviously exceptions and multiple deeper factors to this but the point is that starting is one role, relief is another, and success in either role doesn't guarantee success in the other.
And closers are converted starters frequently, but they're converted starters of a specific kind, the kind with a couple overpowering pitches and a lack of durability, command or secondary stuff to get them through the lineup multiple times. The same attributes that keeps most "born relievers" up in the pen when a team is desperate for starting talent. So basically, not so much "failed starter" as "misfiled as a starter in the hope of developmental progress that didn't come."