But the total amount of magic isn't necessarily the problem. Middle Earth magic doesn't appear the least bit Vancian. Rather, it appears to exhaust the caster, and, more importantly, it can give away the position of one important wizard traveling without an army.
Unsurprising, since Tolkien was writing a story and not designing a game with balance as a primary consideration, but I think it smacked of an unfortunate tendency I noted in old AD&D adventures. (I "blame" the culture rather than the game system. You could run a Fourthcore adventure exactly the same way.) Note that numerous old-school D&D players will see what I'm about to say as a feature rather than a bug

The issue was combat was a puzzle.
Combat in LotR was a puzzle. The heroes frequently find themselves outmatched (eg Aragorn facing nine ringwraiths) and they'll lose unless they find the solution. (In Aragorn's case, he took advantage of the ringwraiths'
extreme fear of fire.) Did Aragorn win by using superior tactics? Maybe, but 9 ringwraiths should be smarter than him. Did he win because he fights well? Definitely not. He won by solving the puzzle.
Maybe Gandalf could have defeated those trolls in The Hobbit, or maybe he couldn't. Said troll captured 13 or so dwarves and a hobbit to boot, so I'm guessing not. However, he could fool them into staying out until the sun came out, turning the powerful creatures into stone statues. Puzzle solved!
I experienced something similar in a Fourthcore adventure we went through. The adventure was called "Murder of the Something Queen" and I downloaded the free adventure after playing. The final boss was listed as a 1st to 3rd level solo (I don't think her actual level was listed, but you can tell based on her attack bonuses and defenses)... but if that was the case she was hideously overpowered. She had abilities that could literally melt PCs in the space of a round, making her a scarier threat than an elder orb beholder (a 19th-level solo!), even though her hit points and "fundamental" stats were pretty balanced.
Having said that, she was a "puzzle boss". The PCs could find up to two one-shot items that could make killing her easier. (We actually experienced an out-of-combat TPK when we failed to solve the puzzle the first time, and ended up creating a new party! The second time we found all the items; it was actually difficult to even find the queen without solving the puzzles, which gave up the items as a reward.) My own PC, a rogue, threw one of the items (an orb) at her, which did 40 or 60 damage plus my Dex bonus plus sneak attack plus Backstab and maybe Weapon Finesse... so 40 or 60 damage from the item and maybe 18 damage from my own abilities, which were as powerful as an E-thief gets since there's no dailies. I felt rather miffed at this, actually, as it meant my own character abilities weren't relevant. We killed her in one and a half rounds, although a PC did get melted. Whether we won or not depended on whether we solved the puzzle. (Personal note: Some people
love to play this way, but I don't think D&D has ever been good at supporting that style of play.)
The movie was into this as well. Near the end of the third film, Gandalf the White leads an army against the orcs. He appears to use a brilliant nimbus of light to blind them, giving his army considerable advantage. Does this mean Gandalf kicked butt with combat magic? Nope. He did that puzzle thing again. Orcs are weak against light. I doubt Gandalf could do more than slightly dazzle an army of humans. (I don't recall how this section went in the books, by the way.)
Gandalf's (and elf-mage) power seemed mainly tied up in "rituals" and utility spells that could have combat purposes, rather than being a blaster, crowd-controller, or what have you. An example would be the heroes fleeing to Rivendell. They had to cross that river. The ringwraiths tried to follow, when a massive blast of water took 'em out. Gandalf later said that the power had come mainly from Elrond and his elf ring (or maybe it was someone else and
her elf ring?) but he had used his own ring to help shape the water (into the form of horses, IIRC).
If Elrond or Galadriel could dish out that kind of combat magic on the field, no one would be claiming they're only 6th-level. However, their combat magic was either weak or non-existent, and Gandalf's ability to set pine cones on fire and chase wolves was considered intimidating. There's currently no class in D&D that could replicate that, not in any edition of D&D I've played (2nd through 4th and playtested 5th, although only once). Although I suppose if Gandalf is a high-level fighter with multiclass wizard training, very few wizard powers and the Ritual Caster feat...
D&D's combat rules make it difficult to achieve a Tolkien-esque feel, because so many tough opponents -- Smaug, the Witch King, a fell beast in the night -- die from a single (maybe-magical) blow or two, but combat isn't necessarily super-lethal overall, and magical healing works largely between scenes.
Smaug was killed via puzzle too, although that one was easy. Sneak in, see the hole in his armor, report on it (did they actually do that, or did Bard make an epic Spot check?) and then narrate how you solved the puzzle.
The Witch King might be a subversion. Yes he was killed by someone figuring out an easy riddle, but I got the impression that he was actually a challenge. Solving the riddle just kept him from cheating. (Of course, it seems it only took two or three hits to kill him.)
I don't remember the fell beast, sorry. Anyone want to refresh my memory?