Our bullpens in the later aughts were generally not comprised of excess pitchers moved to the bullpen. Guerrier is the closest, although he was a waiver claim who only briefly started. Crain, Nathan, Rauch, Mijares, Neshek, Reyes, Breslow, Balfour, Jackson, etc. were all acquired or developed as relievers. The effect you speak of was primarily limited to Rincon and Romero in the aughts, with Hawkins and Guardado being legacy examples remaining from the 1990s too.