In the Language Construction Kit, Mark Rosenfelder makes the claim that case endings 'makes things compact and frees up word order'. The latter is pretty obvious, but do case endings really make things more 'compact'?
I fail to see why. For case endings you still have to add a phoneme or two to the end of a word (well, assuming the language uses suffixes to mark case), which is about as long as many prepositions. Also, many languages with case (though not all) also have adjective-noun agreement, which means that the case ending appears for every adjective and noun that appears in a noun phrase, which can obviously multiply the number of phonemes that the case ending adds to the sentence.
I think it also may be worthwhile to note that the author claims to know Quecha, which has case endings that are all syllables, some of them are even multiple syllables long. I don't know if quecha has adjective-noun agreement or not, but it doesn't really look like it uses any less phonemes than a free-standing adposition. Perhaps the lack of spaces may help a bit, but other than that I fail to see how case endings can make a language more 'compact'.
I should also note that I don't really know any language with case. Well, German does, but only in its personal pronouns. For nouns the case is (typically) only marked on the article. This does save some space since you have a single word (most of which are mono-syllabic) that indicates both case and definiteness, and also number (though very few German nouns rely solely on the article to indicate number, most nouns do have distinct singular and plural forms). Latin, of course, lacks definiteness. Also, it could be said this space-saving is due to inflections rather than case endings. Yes, inflections CAN reduce the number of phonemes in a sentence. Spanish for instance has verb endings that indicate person, number, tense, and mood. And most of these are only one or two phonemes long. An agglutinating language would need a minimum of 4 phonemes to indicate all of this (assuming that each of these could be marked with a single phoneme, which I don't think many agglutinating languages do).