So, sure, fair question why these harmonics and not any of the others?
Well, powers of 2 are out because they are just higher octaves. Then we have a whole series of harmonics that are equivalent ratios to the fundamental when folded down into the octave range (3 (3:2),6 (6:4), 12 (12:8)), (5 (5:4), 10 (10:8)), (7,14,28), (13,26) and so on.
You'll notice the pattern: the harmonics the define the intervals in a 12T system are those that introduce new ratios into the list of intervals, so they lean toward being prime or only having factors not already introduced.
By the time you go through the list, it's easy to see that going up to the 31st harmonic really only leaves out a couple of possibilities from a 12T system: 25, 29, 31 and as far as I am aware this is because introducing them into the pitch class produces results extremely close to already existing members.
And sure, you could go higher, but the pattern will repeat: harmonics whose ratio folded into the octave range are identical, or which give rise to pitches extremely close to pitches defined already.
(in pitch/frequency order) 1st, 17th, 9th, 19th, 5th, 21st, 11th, 3rd, 13th, 27th, 7th, 15th
In harmonic order: 1,3,7,9,11,13,15,17,19,21,27
So, sure, fair question why these harmonics and not any of the others?
Well, powers of 2 are out because they are just higher octaves. Then we have a whole series of harmonics that are equivalent ratios to the fundamental when folded down into the octave range (3 (3:2),6 (6:4), 12 (12:8)), (5 (5:4), 10 (10:8)), (7,14,28), (13,26) and so on.
You'll notice the pattern: the harmonics the define the intervals in a 12T system are those that introduce new ratios into the list of intervals, so they lean toward being prime or only having factors not already introduced.
By the time you go through the list, it's easy to see that going up to the 31st harmonic really only leaves out a couple of possibilities from a 12T system: 25, 29, 31 and as far as I am aware this is because introducing them into the pitch class produces results extremely close to already existing members.
And sure, you could go higher, but the pattern will repeat: harmonics whose ratio folded into the octave range are identical, or which give rise to pitches extremely close to pitches defined already.
It's not a post-hoc rationalization at all.