Carrillio only used tunings based on the division of the whole step. No equal-temperaments outside of those based on the whole tone scale (18tET, 24tET, 30tET, 36tET, 42tET, 48tET, 54tET, 60tET, 66tET, 72tET, 78tET, 84tET, 90tET, 96tET, etc., etc., etc.). I think you may be confusing thirteenth-tones (78tET) with 13tET (thirteen divisions of the octave)
As someone that explores alternate temperaments almost exclusively, I can assure you that it is certainly not a waste of time, and it's certainly not pointless.
Again, as someone who deals with microtones constantly, I can assure you that it is more than possible for instruments to play outside of 12tET. Not just strings.
I don't know Carrillio's string quartet, but the only works of his that I've heard were in 96tET (sixteenth-tones).
I also wrote a clarinet piece that uses microtones. It uses a 31-tone Just intonation, actually. I've also written a bassoon and cello duo in which the bassoon plays a 27-tone "interval-cycle-based" tuning (kinda like Pythagorean, or Meantone) against the cello's 18tET. An orchestral piece that uses quarter-tones in the winds, strings, and brass, 15tET in the guitar, and 21 1/4tET in the electric organ (which is, obviously, not as big of a deal as the others). Plus many other microtonal works (string quartet, tuba quartet, timpani quartet, guitar trio, guitar solo, whatever else I've written...), which have been played.
So trust me, I know from experience that this all is possible!