alt Hacker News> You can, for instance, tune instead to get pure fretted fifths between adjacent strings, and fretted octaves between strings one removed.
No, you can’t. If you tune so that octaves with one string between are correct everywhere on the neck, that will force the tuning to be 12 tone equal temperament, and a fifth in 12 TET cannot be a perfect fifth.
Frets are already on equal temperament on the vast majority of mainstream guitars; you're not getting away from equal temperament unless all you play is open strings, like a koto/harp.
If octaves are perfect with one string in between, the in between string can be slightly detuned from equal temperament to provide a clean fifth, free of beats. Then it also provides a clean fourth up to the octave. That's a useful thing that will make certain chords sound good.