Every verb could be combined with many cases, may be even with all 6, but theses "usages" vary in a semantical sense. As we say , "they answer different questions".
For example, Находить+игрок
Genitive Находить у игрока (недостатки)
Dative Находить к игроку (подход)
Accusative Находить игрока (в пивном баре)
Instrumental Находить с игроком (контакт)
Prepositional Находить об игроке (информацию)
I'd say, every verb is to be combined with specific set of prepositions, and chosen prepositions often dictate the case of the noun that follows.

Is the prepositional case always an option, because one can always throw in a На, О, В after the verb?
Yes, it seems so, though in many cases noun-in-prepositional should not be tightly bound to the verb. For example
Я бросал в лесу окурки
in languages with stricter word ordering could be
Я бросал окурки в лесу,
and then we can say that бросал governs окурки, not лес (that is, accusative as expected).
So yes, if an action is taking place somewhere, we can always specify "where exactly".