To me, the undotted-i thing is more of a hack. Far more beautiful is why Turkish distinguishes the two vowels: Speakers of Turk languages don't like to mingle bright and dark vowels in the same word. Appreciate the economy of not having to switch your enunciation between front and back in the same word.

Speakers of Turkish generally build words with vowels from either of these exclusive groups:

aıuo

eiüö

You see? They could write "ä" instead of "e" to have all bright vowels dotted and mirror the symmetry. But because "e" was already available and pronounced like that in other dominant languages of the time, they stuck to it. No need to break conventions. This didn't work for "ı" because there was no corresponding letter in the Latin alphabet. So they loped off the dot from i and called it a day. A pragmatic decision. Except that the capital version had then to be dotted to keep the distinction. That caused a lot of headaches downstream.