Not really. Turkish has a feature that is called "vowel harmony". You match suffixes you add to a word based on a category system: low pitch vs high pitch vowels where a,ı,o,u are low pitch and e,i,ö,ü are high pitch.
Ö and ü were already borrowed from German alphabet. Umlaut-added variants of 'ö' and 'ü' have a similar effect on 'o' and 'u' respectively: they bring a back vowel to front. See: https://en.wikipedia.org/wiki/Vowel . Similarly removing the dots bring them back.
Turkish already had i sound and its back variant which is a schwa-like sound: https://en.wikipedia.org/wiki/Close_back_unrounded_vowel . It has the same relation in IPA as 'ö' has to 'o' and 'ü' has to 'u'. Since the makers of the Turkish variant of Latin Alphabet had the rare chance of making a regular pronunciation system with the state of the language and since removing the dots had the effect of making a front vowel a back vowel, they simply copied this feature from ö and ü to i:
Just remove the dots to make it a back vowel! Now we have ı.
When comes to capitalization, ö becomes Ö, ü becomes Ü. So it is just logical to make the capital of i İ and the lowercase of I ı.
Yes it's hard to come up with a different capital than I unless you somehow can see into the future and foresee the advent of computers, which the Turkish alphabet reform predates.
Of course the latin capital I is dotless because originally the lowercase latin "i" was also dotless. The dot has been added later to make text more legible.
> low pitch vs high pitch vowels where a,ı,o,u are low pitch and e,i,ö,ü are high pitch.
Does that reflect the Turkish terminology? Ordinarily you would call o and u "high" while a and e are "low". The distinction between o/u and ö/ü is the other dimension: o/u are "back" while ö/ü are "front".
> Does that reflect the Turkish terminology?
Yes. The Turkish terms are "kalın ünlü" and "ince ünlü". They literally translate to "low pitch wovel"/"high pitch wovel" )(or "thick wovel"/"thin wovel") in this context.
There is a second wovel harmony rule [1] (called lesser wovel harmony) that makes the distinction you pointed out. Letters a/e/ı/i are called flat wovels, and o/ö/u/ü are called round wovels.
[1] https://georgiasomethingyouknowwhatever.wordpress.com/2015/0...
So, instead of adding two full letters, with proper upper case and lower case, you added two halves to hack Latin alphabet. This is the bug.