Combine detail #101 with a system where different nouns (and ~adjectives, obviously, as detail #101 presupposes a vague or nonexistent distinction between these two classes) belong to different declensions, mainly determined by morphophonological things.
Thus, case distinctions will come and go rather randomly for phrases - "that old man" might distinguish dative-genitive, accusative, nominative and instrumental, but "that young man" might distinguish dative, genitive-instrumental, accusative-nominative, and "this learned man" might distinguish dative, genitive, instrumental and accusative-nominative.
Thus, the amount of cases distinguished in the language would get somewhat perplexing.
We add to this that with deictic determiners involved, some adpositions might be left out - yet the case goes on whichever noun in the NP attracts case most strongly, so "at this X house" ≃ "here X house" -> that X.at house/that X house.at, depending on what X is. For some nouns, the deictic determiner may even be the highest-ranking attractor, in which case "that.at(≃there) X Y" would be the outcome.