That's actually the crux of the issue: if you fret the note to tune the next string, then you achieve equal temperament at the expense of any inaccuracy that co

That's actually the crux of the issue: if you fret the note to tune the next string, then you achieve equal temperament at the expense of any inaccuracy that comes from all sorts of things like imperfect action height, imperfect bridge tuners, excessive pressure beyond just contacting the fret, sideways motion, etc. which is all avoided by using open strings instead. But then doing open strings by ear doesn't get you equal temperament, it gets you integer ratios instead. Open strings with an electronic tuner gets you the best of both worlds (assuming you want equal temperament).