Well, I think you can get closer to authentic Middle-Earth simply by keeping Mentalism and ditching Channeling if pruning to two realms. Only the "Morgoth element" really seems like consistent Channeling for dark magic and that may be as well represented with Evil Essence, as it a pervasive corruption of the world. Any Channeling lists really desired can be moved to one of the other realms.
The idea that Middle-Earth is a very low magic setting is based largely on the Hobbit and LotR, though there is some powerful stuff there, too, if a bit more subtle most of the time than D&D magic. But that is a view from the perspective of a people without magic of their own, at a time when magic is on its way out and less common even than earlier in the Third Age. The First and Second Ages would have had a lot more powerful magic-wielders around. Gandalf appears weaker than he is because until he returns as Gandalf the White (not from some spell, but direct divine intervention), he is bound by restrictions on his use of power to avoid his corruption. Having been found worthy and freed to use his abilities, he freezes some pretty mighty folk in place, fires off some kind of laser blast type attack, and casts buffs on armies. Sauron literally coordinates a huge army and puts the fight into a large part of it, controls his own private volcano, and manages to crack the sanity of Denethor, a strong-willed man with Mentalism type abilities in his own right. Even in this twilight of the elder days, with Elves and magic departing, there is still quite a bit of wonder, though it keeps its head down with Sauron active. Just going back to when Sauron isn't around would justify more open magic use, but only the dark powers seek to extend their influence by channeling their power into servants.
Magicians aren't really that bad a fit, once you consider the off-screen battles between Gandalf and the Ringwraiths or Gandalf and the Balrog. Those clearly involved unleashing some flash and bang spells.
Middle-Earth isn't a place you should expect a spell-slinger in every party of adventurers or every little village, but they don't have to be super-rare, either. The earlier you go, the more powerful the magic and those wielding it. Nobody is throwing up a mountain range just to hinder migration in the Third Age. But even as late as LotR, magic was used to raise a river as a weapon against powerful undead, shield the realm of Lorien, and put on spectacular fireworks shows that would wow us today. Saruman appears to be able to use birds as spies from hundreds of miles away.
I would say that less-flashy magical professions should be more common than the showier ones, and semis more common than pure casters, but I certainly wouldn't forbid the playing of Magicians or Illusionist if someone wanted to play one. There's justification in the texts, if you want it. I'd switch Ranger to Mentalism and if I kept Animist, move it to Essence. Cleric and Paladin don't really fit.
