Many musicians can readily confirm that the difference between temperaments can be felt and heard by trained ears. A guitar tuned to equal temperament has major thirds that warble audibly. It feels different when you use just intonation, which isn’t generally possible on a guitar.
Why can’t you use intonation? Isn’t that just confirming the note is the same on different strings? And also the goal of bridge adjustment?
For the reasons the article explains. You can use “just intonation” a bit on a guitar, but it will only work for certain chords in certain positions. BTW note that just intonation is different from string intonation - I wasn’t talking about making sure the 12th fret is the same note as the 12th fret harmonic on a single string, I was talking about the tuning system called “just intonation” that defines what certain intervals are, and allows for perfect thirds and perfect fifths in some keys. But it won’t work everywhere on a guitar. It’s not possible to get (for example) perfect fifths on all string combinations in all positions, but it is possible to tune the guitar so you have a perfect fifth when crossing 1 string while in 5th position.
The goal of regular guitar intonation and bridge adjustment is to get the guitar as close as possible to 12 tone equal temperament (TET), which is slightly ‘out of tune’ as the article describes. 12 TET is the best you can do if you want something equally close to perfect fifths (or thirds, etc.) in all positions in all keys across all string combinations; that’s what 12 TET is for, it’s designed to minimize the worse case, at the expense of losing the best case.