It is true the cover may transmit air-borne vibrations to the stylus/disc interface.
But it may also be true that it shields that interface from those vibrations by acting as a a barrier whose micro flexures absorb them.
Anyhow my TT has no cover so I can't hear it. Plus it doesn't seem to become inordinately dirty.
I think many audiophiles over-analyse. That is ANAL ise.
And hands up please anybody who has observed any tracking weight variation at all with lid up or down using an electronic scale that measures to 0.01 gramme??
So let's kill that one right off.