This isn't an assumption. It's an empirical fact. Almost all music around the world uses a diatonic or pentatonic scale. The pentatonic favors such intervals even more strongly. The odds against this happening, if there were even one other equally-good possible non-harmonic scale, are astronomical. QED.

The work presented in this comment (link to audio examples) makes a convincing case that the consonance of "diatonic" scale intervals is simply an artifact of common timbres/sound spectra (which in turn are due to the physical makeup of most musical instruments), combined with familiarity. The music presented there sounds "consonant" and "harmonious" to me in a way that most atonal music simply doesn't.

(I am linking 4hodmt's comment here only because it's directly relevant and I don't expect its author to join this subthread. Any upvotes should be directed there.)