At the risk of exposing myself to jibes about having a tin ear, I will confess that I find myself making extensive use of a low open E when playing for example in Eb. Mostly as kind of a ghosted pedal, or for articulation/phrasing. It can sound good to me, kind like a blue note. Low pitches are psychoacoustically more difficult do distinguish, and this is what I hypothesize is what makes this not sound like a mistake.

Anybody else notice this, and more to the point, use it to musical advantage?

Dude-
Jamerson did this all the time on all those '60s Motown albums/songs.

...and yes, IMO, it is very effective.
;)

I'll play a palm muted open string as a ghost note in walking lines too.