I'd always have this argument with the rhythm guitarist of my band on stage. He'd stop and tune by ear to himself by harmonics

1) You're annoying the audience. Stop.

2) You're only tuning to yourself, not the band. Please use your tuning pedal.

Yeah, but that's always the best you can do without an external note. And if there are no external notes around, you could argue it's all that matters;)

Especially since A=440 is arbitrary to begin with.

It starts out arbitrary but becomes useful once everyone agrees with it, like measuring distance in meters- which has gone through several definitions, none of which make much sense in terms of being based on a natural constant and using a nice round numbers as a coefficient.

If four instruments are following the standard and one is a bit flat because "A-440 Hz is arbitrary" then the whole band sounds like a mess.

Sometimes people intentionally want the effect of a guitar that's in tune relative to itself (which provides harmonies and aesthetic value) but not necessarily on the normal scale or relative to other instruments.