The specific use case for equal temperament is more or less how do make a fixed tuning instrument sound "good enough", without resorting to a very large amount of keys or buttons to adjust the tuning so the chords sound right. Although it was developed around Western music, I don't think that Western scales per se are necessarily the constraining factor.
Certainly just intonation sounds more pure on a fixed tuning instrument if you play within the constraints of the tuning ratios chosen. Step outside those constraints, and the sound is usually pretty awful.
12TET also has some "musical usefulness" on its own. The system introduced a sort of tonal ambiguity in modulation -- the commas that normally result in a more just / Pythagorean type style (https://en.wikipedia.org/wiki/Comma_(music)) get "blurred", and this is a characteristic musicians can exploit. Furthermore, in my experience, for sounds with lots of overtones (sawtooth synth waves, distorted guitars, etc.), that slightly detuned third in a 12TET trichord ends up sounding "thicker" for a lack of a better word, with the detuned beating more adding to the texture. This is best heard on a synthesizer where it's easy to flip between two tunings: to me, that, say, 1980s "power chord sawtooth stab" type of sound just doesn't sound as "thick" in just tuning, in my opinion. (In fact, when programming a synthesizer, people often slightly detune oscillators for this exact same reason!)
Nonetheless, it would be interesting if more "adaptive" type just intonation type systems came out that more approximate what non-fixed pitch instruments do (adjusting the notes to a "correct" your tuning during any modulation). Pure sounding triads also are useful, and you really can't do it super exact with 12TET, it's always "good enough". :) Hermode tuning is the only major one I know of, it is implemented in some synthesizers and DAWs. I haven't tried it yet -- my bet is you still would be a bit constrained (no dramatic 20th century classical type of chromatic modulation or the like), but you'll gain some freedom to modulate compared to a fixed just tuning setting.
Certainly just intonation sounds more pure on a fixed tuning instrument if you play within the constraints of the tuning ratios chosen. Step outside those constraints, and the sound is usually pretty awful.
12TET also has some "musical usefulness" on its own. The system introduced a sort of tonal ambiguity in modulation -- the commas that normally result in a more just / Pythagorean type style (https://en.wikipedia.org/wiki/Comma_(music)) get "blurred", and this is a characteristic musicians can exploit. Furthermore, in my experience, for sounds with lots of overtones (sawtooth synth waves, distorted guitars, etc.), that slightly detuned third in a 12TET trichord ends up sounding "thicker" for a lack of a better word, with the detuned beating more adding to the texture. This is best heard on a synthesizer where it's easy to flip between two tunings: to me, that, say, 1980s "power chord sawtooth stab" type of sound just doesn't sound as "thick" in just tuning, in my opinion. (In fact, when programming a synthesizer, people often slightly detune oscillators for this exact same reason!)
Nonetheless, it would be interesting if more "adaptive" type just intonation type systems came out that more approximate what non-fixed pitch instruments do (adjusting the notes to a "correct" your tuning during any modulation). Pure sounding triads also are useful, and you really can't do it super exact with 12TET, it's always "good enough". :) Hermode tuning is the only major one I know of, it is implemented in some synthesizers and DAWs. I haven't tried it yet -- my bet is you still would be a bit constrained (no dramatic 20th century classical type of chromatic modulation or the like), but you'll gain some freedom to modulate compared to a fixed just tuning setting.