I have the same tuner and really like the mute feature. (I picked it for that reason after hearing a really good guitarist retune in the middle of a live gig.) I had never thought of your points about bass needing to be in tune as the foundational instrument. Our guitar player likes to say "close enough; it's rock and roll!" and I believed him. Now I have a retort! That said, I have been the one to stop the rehearsal of a song after a few bars when I hear something (very) wrong: the rhythm guitar left his capo on from the previous song! XD