There are several other temperaments like 19-TET and 31-TET, but almost all modern music uses 12-TET. Why aren't the two former used more often?
What would the motivation be? Either you have an instrument with fixed pitches like a piano, and then it is not practical to play in anything other than 12-TET. Or you don't, and then it is more compelling to play in locally converging pure intervals.
19-TET or 31-TET make mainly sense with synthesized music, and even then many synthesizers use the 12-TET based MIDI or a piano keyboard as their language of talking about pitch.
That makes for quite an entry threshold that will mainly be crossed by people obsessed with tunings, and that's at best a comparatively small fraction of composers, and not really a major interest for most of the audience.
The good enough is the enemy of the better, and 12-TET is good enough for most. And those not satisfied with it will more often than not rather lean towards well-tempered tunings than equally tempered ones.
Using an equal temperament makes it practical to transpose music into arbitrary keys without affecting which intervals are consonant and dissonant. When using non-equal termperaments, transposing most pieces of music into at least some keys would result in consonant intervals becoming dissonant, dissonant intervals becoming consonant, or both.
An advantage of 12-TET is that it includes pitches that have perfect 2:1, 4:1, and 8:1 ratios, and almost perfect 3:1 ratios and 6:1 ratios, without needing an excessive number of pitches. The only ratios below 8:1 that are not accurately represented are 5:1 and 7:1. While a 29-tone or 41-tone equal temperament could offer even more accurate 3:1 and 6:1 ratios, subdividing each octave into 29 or 41 pitches would be much more awkward than subdividing into 12.
- The harmonic and melodic language is more familiar, and change is difficult to introduce.
- Instruments are generally designed for 12-TET.
- There is an enormous body of music that uses microtonality — almost all non-Western music does — but it remains less known in the west, and it doesn't use systems like 19- or 31-TET.
- For Western music, not much is actually gained by using other temperaments. The music that does use it tends to focus on musical elements other than melody and harmony: timbre, rhythm, individual intervallic sounds.
- Popular music, in particular, relies on a common musical language to appeal to the largest possible audience. For rock'n'roll and its descendants, that's 12-TET. It's conceivable this could change eventually with the rise of electronic music, but it will be a long time coming.
It depends on what you listen to. In recent years I discovered how fun it is to play fretless instruments and then I actively searched out music in other temperaments. I am doubtful I would have even heard about them if I hadn't begun playing these instruments myself. So I wouldn't be surprised if it is simply because people do not know about it.
We have a 12-tone system because no one can find a better number.
If we lost all music, it would return in the same form with the same musical key structure.
In the same way, if we lost standard tuning on guitar, it would come back again because no one can find a better tuning.
There won't be any new tunings on guitar that are more successful.