For those that don't know Turkish, there is a faced of the language called vowel harmony. When suffixes are added to a word, which is common in Turkish for everything from pluralization, verb congugations to prepositions, the vowels in the suffix will be altered to match the last vowel. (Some Arab loanwords don't follow this, mind you, but it works 98% of the time.) So, the dotted and undotted vowels (except e for some reason) all follow this pattern.
(Incidentally, however, the problems could be solved by turning the single dotted i into a double dotted I, keeping the original symmetry. At that point, a lowercase dotted I would no longer break any system, since you could map them to be functionally equivalent for anything after the reform. While we're at it, I have a few ideas for English language reform...)