With all due respect, I think you may be underestimating the amount of training that you would need. My sister has perfect pitch, but only really honed her skill at it after ~5 years of music theory/ear training classes. That was about when I learned to identify intervals by ear.
Singers also get "real pitch," I think, and in general, when you know the sound of an instrument's registers really well, it can be a hack for professionals to turn their relative pitch into "perfect pitch."
Also, FWIW most professional musicians I know can't tell whether their A is sharp or flat by a few cents (eg the difference between 440 and 442), but they can tell interval size immediately. The interval sizing tends to determine "out of tune" rather than the frequency of the A.
Singers also get "real pitch," I think, and in general, when you know the sound of an instrument's registers really well, it can be a hack for professionals to turn their relative pitch into "perfect pitch."
Also, FWIW most professional musicians I know can't tell whether their A is sharp or flat by a few cents (eg the difference between 440 and 442), but they can tell interval size immediately. The interval sizing tends to determine "out of tune" rather than the frequency of the A.