Regarding multiple players, I don't think the average orchestra would take very long to tune. And in a session people rarely arrive at the same time anyway. I agree there is some justification for a using a tuner in a band using amplification, unless, like some rock bands, the tuning is part of the performance. But (for strings at any rate) it's easy enough to press part of your instrument to your ear, and you hear it above all others.
If there's an instrument present that cannot change pitch without being taken apart and rebuilt, it seems to me totally daft not to tune to it, rather than your black box.
Leenia - obviously the harp is a different beast, presumably you would tune in different temperaments according to circumstances; which is a long process by ear counting beats, and needs quiet surroundings; but I'm sure I've read that in the past it was normal for the performer on a harpsicord on to partially retune between movements in different keys, to shift the "wolf", so perhaps harpists would have no more difficulty doing this? And surely your guitarist would tune to one or other of your harps if because of a change in temperature your pitch was not quite 440 or whatever you adopt.
Lonesome - unless someone is auditorially challenged, or whatever you want to call it. the fact that they're out of tune with everyone else suggests that they're not listening to what they're playing. Which is why they need to throw away the tuner and start to listen; and a quiet word in the ear may be appropriate. Maybe suggest that their electronic tuner may have a fault (perhaps it actually has!)