It absolutely blows my mind how people can come into homebrew forums and demand that all concepts being bandied about line up with their own tastes and opinions. Did you see me losing my mind over that Magical Girl class a few weeks ago? No, because if someone wants to do something I think is stupid, that's their right. My opinion only matters insofar as it helps them reach their goal. Saying, "Your goal is stupid and you should stop it" is a waste of everyone's time. Get over yourselves.
ANYWAYS.
I totally get what you're shooting for here. And yes, it's absolutely something supported in fantasy literature and whatnot (not that it actually matters if it is or isn't).
As far as implementing it goes, I'm definitely of the opinion that what you're shooting for could be handily accomplished by re-fluffing the wizard. Rename/refluff class features, rework some subclass options a bit to align with cleric domains, and have them use the cleric spell list. I'd probably also work on redoing or just refluffing a few key wizard spells (change damage type and some other small aspects of them) to work for clerics; i.e. Shield, Mage Armor, and maybe a couple of decent damage spells like Fireball or Scorching Ray (lower the damage a bit, make it radiant, etc.).