First of all when the turkish alphabet reform happened there was a big revolution happening, and most of the people were illiterate. Also, the ottoman alphabet was incredibly bad for writing turkish (among many causes the language has eight vowels and vowel harmony) that nobody in their right mind would oppose.
Secondly the empire was not ancient at all, in fact what Ataturk completed was started by illuminst sultans like Mahmud II and Abdulmejid I. Also, Turkey is not a continuation of the empire but the last of the states that liberated itself from it.
More pragmatically, I'd express it as "using any mix of uppercase or lowercase letters wouldn't obscure or change the word being expressed". (I'm sure there are exceptions where you could conflate a proper noun with another noun without proper capitalization, but since you don't get capitalization in speech, people generally can deal with it.)
e: Thinking slightly more, I'd probably phrase it as "52 symbols map to 26 letters, and the words of the language are defined in terms of letters."