It's possible but for anyone who would actually care to acquire it (i.e. musicians), relative pitch is just as useful for any task that matters and much easier

It's possible but for anyone who would actually care to acquire it (i.e. musicians), relative pitch is just as useful for any task that matters and much easier to acquire. Most acquire it by accident. And arguably, perfect pitch isn't desirable anyway, since standard 12-tone equal temperament is not the "perfect" form of music by any measure. The tuning basis of 440hz is completely arbitrary, and there are plenty of examples of the tuning in any genre being changed (usually to a higher pitch) for excitements' sake. Plus, mathematically any form of dynamic just intonation is superior to fixed 12-tone equal temperament. Relative pitch remains useful in these contexts, while absolute pitch does not.