If you want to get right down to it, Gary Gygax is at least as important as Tolkien for determining the shape of today's standard fantasy novel. The wizard in training archetype never and never would have appeared in Tolkien's work by the very nature of wizards. But it is of course central to the game of Dungeons and Dragons. Everyone wants to play as a wizard, but if they are quasi-angelic beings then of course they could not be in the same group as warriors in training or else that would unbalance things. So wizardry became a profession. This is also true of the motif of priests in fantasy novels. Note that nearly every fantasy novel today is polytheistic, but in the Lord of the Rings noone even mentions a god (though in fact, there is exactly one god of Tolkien's universe). The modern practice ultimately stems back to the cleric class, I think.
I wonder what today's fantasy would have looked like had Dungeons and Dragons never been invented.