I suspect that it might have something to do with tonality and functional harmony. A diminished or augmented tonic chord, due to dissonance, would be less satisfying and conclusive as the final chord of the piece than a minor or major chord - therefore the fifth degree has to be perfect. A high seventh degree makes the resolution to the first degree more satisfying, which is why the seventh degree is often raised in minor.
However, those constraints still leave us with many scales other than natural major and harmonic and melodic minor. (For example, Lydian scale.) Is there something else, other than a consonant tonic chord and the high 7th degree, that makes the major scale and harmonic and melodic minor scales particularly suited for tonal music - and this something is lacking in other scales?