Eric, you certainly have a penchant for asking tough questions that really don't have any clear answers
I'm not even gonna try to address most of this in detail
I plan to simply accept this and will try to learn as many of these 'proper' combinations, but I'm curious as to the reasoning behind it.
Good, that's the best way, really
But your statement here reveals perhaps where the problem lies: "reasoning behind it". If I were to make a Gross Generalization, I might say that as a student of Latin, it might make sense that you are looking for rationality and structure in language. Latin (the way we study it nowadays) certainly seems to provide this stuff in spades
But that's not really how a living language is. In any case, it's not something designed or engineered (1), such that one can ask for the reasoning. To paraphrase a well-known saying: Language happens
So.... you've got your work cut out for you!
(1) You could hold up Esperanto as an example of an engineered language, and certainly it has been fairly successful. My understanding is that one of the basic tenets of its design is that it is completely regular, to make it easier to learn. I've heard (this is pure heresay and possibly apocryphal) that young children who have grown up in heavily Esperanto-speaking households have begun to introduce irregularities
into it, which of course drives their parents crazy, because it breaks the Grand Design of the language! If this story is true, it tells us something very interesting about "Language with a Capital L"...