Arguably, in a hospital where everyone wears scrubs, the lab coat has no functioning other than as a symbol. It used to be what people threw on over their street clothes when entering a laboratory so as to avoid ruining their clothes, but obviously, doctors generally don’t wear street clothes anymore, at least in hospitals.
As for the stethoscope, I suppose one could argue over whether it is so essential that they have to keep it on them at all times rather than having one available in the room, as with all the other paraphernalia. That is probably a different calculation for each specialist. A cardiologist would probably want one, an ophthalmologist probably not.
