Classically trained musician without absolute pitch here. I would say yes and no to your comment. My undergrad degree was in flute, and I can assure you that absolute pitch can be quite helpful for wind players especially. My teacher had it, and would be able to tell you if you were out of tune even if you hadn't played with a piano or other reference point.
On the other hand, I once sat between two flutists who both claimed to have absolute pitch but were playing out of tune relative to each other (and each refusing to adjust to the other since... they had absolute pitch). So, it doesn't actually mean you're going to be perfect.
By "inexpensive electronic tools," perhaps you mean these tuners that you can attach to guitars and whatnot? These are certainly helpful for stringed instruments, but are basically irrelevant if you play a wind instrument. Most musicians with relative pitch only need a single reference note and then they're ok. Where relative pitch tends to fail you, however, is over longer periods of time when the pitch tends to drift. You hear this in lots of school orchestras. The pitch will tend to drift upwards (at least in the strings) over a long work. Here, no mechanical/electronic device is going to help you.
My brother and I are both musicians with perfect pitch, and we've found it useful in a variety of circumstances. To name a couple, it really helps if you're jamming and want to pick up a progression quickly, or if you're DJing and want to key match. I will concede that Traktor recently got key detection, which is nice, but especially when playing live I find that key segues will pop into my head without having to search for the next song in the right key.
Even the best relative pitch cannot help you exactly memorize a melody -- if you are unable to remember what note it actually starts on, you haven't remembered it fully.
If you're saying that perfect pitch and relative pitch are different things in that it isn't as if perfect pitch is better than relative pitch, then yeah, I absolutely agree. The hacks that I mentioned involve perfect pitch specifically, but transcription ability like you mention is probably tied most to one's sense of relative pitch, even if one has perfect pitch.
Are you referring to someone else's comment? I use them interchangeably in the first paragraph
If you listen to how people with absolute pitch describe their experience, you will realize that they are experiencing perceptions that you cannot. That is interesting.
edit: I suspect this conversation won't lead anywhere because there isn't good language to talk about phenomenology. But I think we both understand the other's hypothesis.
Perfect pitch is a real-life superpower for musicians. I'll grant, like another commenter said, that if I had child-like neuroplasticity, attaining perfect pitch would just be icing on the cake.
Relative pitch is just recognition of intervals between notes and the qualities of different chords, but you're right in that perfect pitch and relative pitch are quite unrelated.
Since the intervals (not frequencies though) between scales are consistent regardless of the pitch of the tonic, one could compose a piece using relative pitch that they believe to be in the key of C, when actually they are "hearing" it in Bb. Precise relative pitch ability has much more utility in composition, absolute pitch would have more advantage for performance (choral starting note, woodwind tuning, on-the-fly assessment of string fingering).
It would only be useful if for some reason you needed to compose and then perform a piece without a reference pitch.
I believe that people confuse it with relative pitch which usually translates to the skill of transcribing and memorizing melodies. This is very useful as a musician or even in daily life sometimes. There are people who have an innate talent for that too, but it's unrelated to perfect pitch.