I'll take this one step further by noting that, prior to the introduction of Expert classes in D&D 3x, the vast majority of NPCs (to say nothing of priests specifically) in offical AD&D/D&D supplements were actually classed characters (e.g., Clerics, Magic Users, Fighters, etc).
Some of the 2e stuff got pretty crazy about it too. Every single city had to have a few high level wizards, and the high priest of every temple had to be 12th to 20th level, even if it was a smallish city / faith and an 8th level Cleric could easily have handled things (and created the possibility that one would have to go further to get access to something like Raise Dead).
I very much liked the Eberron notion of more Adepts and Experts and Aristocrats in the clergy, and less Clerics. (Bards also make handy priests, with some healing, some evangelizing and some lore-mastery.)
One thing I would want to do would be to make the Heal skill more effective in a Cleric-light clergy situation.