So power chords sound so good because they're very close to the just 2:3:4 chord, and when you distort the 2:3:4 chord, the intermodulation of the frequency components produces new frequency components that mimic a harmonic sound with a fundamental at the GCD of the 3 chord frequencies. For instance, if you play 200 Hz, 300 Hz, and 400 Hz and then distort it, the sum and difference frequencies produced include 100 Hz, and otherwise line up with the existing harmonics, producing a tonal sound. For other chords, this doesn't work as well, because the guitar is tuned in 12-tone equal temperament, so the harmonics of the original notes don't exactly line up with each other and, after distortion, there are more intermodulation products, even less lined up with each other.
In just intonation, chords are made of small integer frequency ratios, so all the tones in a chord are always harmonics of some other tone, meaning their harmonics line up pretty well (except for the inharmonicity of plucked strings), and if you play it through distortion it will produce a tonal sound. For instance, if you play 600 Hz and 700 Hz and then distort it, it will produce new frequencies at 100, 200, 300, 400, 500, etc. and produce a tonal sound at 100 Hz.
So this is dyads made from the harmonic series, first in piano, then undistorted guitar, then distorted guitar (where they all produce basically the same tonal sound).
Sound is FlameStudios "Telecaster Direct In" soundfont, TSE 808 distortion, FA3 amp simulator, JJ Powertube Impulse response.
Please criticize my guitar tone.