You raise an interesting question whose roots quickly descend into murky ground
...indeed I do. And to go further: how did cases originate anyway? I'd assume there are several theories. It seems to me that cases are more numerous in older and more synthetic languages.
Oh, gosh. Look at Finnish! 15+ cases, depending on how you count. Most of them match pretty nicely to prepositions with motion or location.
Accusative (or so I have heard/misunderstood...) evolved out of the idea of motion towards a thing - so another relationship.
I suspect not. In some languages the direct object is marked with a preposition, one quite different from prepositions for motion.
(This may be very very wrong... I'm only hypothesising from my moderate knowledge of languages...)
There's a technical term for what happens when words go from being parts of vocabulary to being for grammar only. It's "grammaticalization." Google on that for articles galore.
For example, in English the verb "will" has lost most of its use meaning "to want" and is used by far the majority of the time for the future tense. The future tense in several Romance languages come from the infinitive + a form of habere, then they all mashed together into a conjugation.
I'm not sure we can say where each Indo-European case came from (doubtless many have speculated freely), but I think it's safe to say one or two probably started out as postpositions (rather than prepositions) that merged with the noun stem. I think genitives have a tendency to evolve out of adjective derivations.