You are quite correct. The "saxon" apostrophe-s isn't a full genitive case. It doesn't work the same way as the case system in Latin, German or even Anglo-Saxon.
The 's can be described as a "clitic". A "little" word that "leans" on another word or phrase and so functions at the same level of syntax that "of" functions at. Clitics are unstressed, and in the case of 's, lacks any vowel.
And while analogy doesn't prove anything in grammar, just as you can say "the contributions of Paul, Mark and Luke" (you don't need ".. of Paul, of Mark and of Luke). You only need to use the 's once.