I couldn't find the examples I had before. I know they were somewhere on the turkish -> english duolingo. I think I remember one like "bende kizlar" = "I have the girls" or something. And it seemed like if you had some something, you would use the possessive, but if you had specific ones of something, you would use -de.
The "'da" suffix is locative, "Ankara'da means "in Ankara" so you can't lose that in translation. "Var" by itself also doesn't show possession, it just means "there is", it can be used to show possession if you say something like "There is my X", or in this case, "There are Ankara's lots of cats". I believe it'd be something like "Ankara'nın çok kedisi var", and that's only if Ankara literally owns the cats.
Anyway, "Ankara'da çok kedi var" can mean the same thing as "Ankara has a lot of cats", but it is important we understand the difference, and this is a locative lesson, so we have to translate the locative.
there is nothing wrong with the sentence, and we are not teaching sentences, you are not supposed to memorize sentences, you are supposed to understand sentence structures in Turkish, and learn words. Also understand that this is not an encyclopedia. Feel free to use Turkish wikipedia for that.
I don't think there is a problem with this sentence. However, with all due respect, I have to strongly disagree with you regarding your proposition that you "are not teaching sentences". When one teaches a language, you don't just teach grammar and sentence structure (syntax). The text you employ (be it spoken or written) should be meaningful and relevant to the learner. I could have learned much more if the examples provided were not about turtles drinking milk or eating lemons in the west! Please reconsider your approach...