Mark Liberman has pointed out that the languages of the "barbarians" who defeated Rome were well endowed with cases, which demolishes the proposition that it was the case system of Latin that did in the Romans. The same point can be made the other way round. The Roman Empire not only had an end, it had a beginning. The Romans, with seven cases, began their expansionist career by defeating speakers of other Italic languages, such as Faliscan, Oscan, and Umbrian, all of which had the same or fewer cases. As they expanded out of Italy, they overcame, among others, speakers of Greek, with five cases, Punic, Aramaic, Arabic and other Semitic languages, with a maximum of three cases, and Egyptian, with no case distinctions. The case system of Latin doesn't seem to have enfeebled them in the least.
We might also enquire about the inflection of the languages of other great military powers. The greatest empire the world has ever known was that of the Mongols. Classical Mongolian had seven cases, all clearly distinguished, in contrast to Latin: nominative, accusative, dative, genitive, ablative, instrumental, and comitative. Somehow this impediment didn't stop them from conquering most of Eurasia, including the caseless Chinese.