Perfect pitch is overrated. In college as a music student with excellent relative pitch, I routinely outscored peer students with perfect pitch when taking classical ear training courses. Perfect pitch is more of a parlor trick. It's occasionally useful when trying to tune a stringed instrument by yourself, and distracting if your ensemble starts to drift off key while remaining in tune with each other.
Also, trained relative pitch is better than untrained perfect pitch. For instance, if my instructor played four bars of a four-part bach chorale on the piano (sixteen quarter notes, perhaps a couple of eighth-note passing tones), I could fully notate it within three repetitions, sometimes on first listen - if I were initially told what key it was in. Someone with untrained perfect pitch would be able to tell if the instructor was lying about what key it was in, but they wouldn't be able to notate it. So in that scenario, the only thing it's useful for is recognizing what key it's in. If I hadn't been told, I could have just notated it in C and then transposed it to the right key later.
I would later learn that being able to notate a bach chorale by ear is nothing compared to the kind of ear skills you need as a jazz musician - but again, there, perfect pitch isn't important or super useful. We learn chord relations - it's all relative.