So this wont' contribute much to the why, but this is my idea on why the casters are based the way they are:
Wizard: Obviously why; they learn their magic, so they need a high int to understand what they are casting
Warlock, paladin, sorcerer: Notice that all of these are based on dieties to an extent. Clerics get their power from their gods and goddesses, Paladins get their power from their oath (usually sword to a patron or diety), and Warlocks get their power from a diety in most cases. So I feel the idea behind this, is that you need Charisma to use that magic since it is based on your patron/diety allowing you the powers to cast those spells. The higher the charisma, since this stat is used for social interactions, the more powerful the diety/patron allows your spells to be. Of course a Sorcerer is a bit different, it is innate rather than gifted (usually), so they are the outlier here.
Cleric, Monk, Druid: The wisdom classes make sense to a degree, though I feel like Cleric could use Charisma since their casting is diety based. However, these classes need to be wise in the world, they have a deep understanding of the weave, I feel like--almost an innate knowledge. Think the wise druid who is in tune with nature--or the wisened old Monk in tune with the Ki energy around him.
I think these are why the classes casting skills are put the way they are by and large.
