Gabriel S. answered 05/21/19
Columbia University Music Major
Much of this question has to do with the the aesthetics of music more than the theory. A Natural minor scale and Phrygian scale simply sound very different from each other. The Aeolian happens to be what musicians favored as the basis of the minor sound. I think it's good to clarify that the idea of modes predates the idea of major and minor. Ionian and Aeolian may correspond closely to the modern day notion of major and minor that evolved roughly after 1750, in antiquity there was no such classification.
Let's look at this close. From harmonic theory (again developed after the era of modes), we know that the relative minor of a major key can be derived from the 6th note of the major scale. This happens to correspond to the Aeolian mode. So even though Phrygian mode might have more minor intervals than Aeolian, the Phyrgian sound with it's flatted second is quite different from what became established as the natural minor sound. The Harmonic minor scale( which is the Aeolian scale with a sharped 7th) grew out of attempts to reconcile the Phrygian with the minor sound. A lot of this came out of counter point rules that evolved in the Renaissance that deemed some intervals more preferable than others. In the system of counterpoint developed, the old modes fell out of fashion as they often created intervals that were not favored in the system. (If you are interested in counterpoint the Phrygian flat 5 cadence is a good example of what I am talking about.)
Here is a good place to say that none of these scales were consciously chosen but evolved over time as musicians developed common ideas about what kind of music was most pleasing. These ideas changed significantly over time and are continuing to change today. Sorry for the long winded answer but there was a lot to unpack from this seemingly simple question. I hope this helps.
Best,
-Gabe