Perhaps what is needed is a tuner that, if a note is played on an instrument and the tuner is told for example "that is a Bb", will automatically adjust itself so that the pitches it checks are in tune with that input.

On a more academic note, one problem is the different temperaments instruments are tuned to. My understanding is this. Keyboards, and guitars (because the fret spacing has to apply equally to every string), are tuned in equal temperament. Equal temperament is where each interval is a bit out of tune, but this is spread equally over every key. Recorders, whistles, melodians and concertinas are tuned in one of a number of "meantone" temperaments, where some intervals are closer to what we feel as "in tune" than others, (which produces the sweeter sound of a melodian compared to an accordian). And then there are instruments that are not fixed in pitch, eg trombones, fiddles of various flavours, and voices, which produce intervals (fairly) accurately judged from a heard or remembered bass note.
Thes factors combine to produce anything from an exquisite discord and its resolution, to the sound of folk musicians playing after a few beers.

Intervals are what matters, ie the difference between two pitches. Pitch itself is irrelevant, except to instrument makers trying to achieve the ultimate sound.