[Pitchwife]

Before I come to davem's central question, I'd like to address two not-quite-so-central points that came up during the course of this discussion.

1. The matter of Sam and the trees. I think this needs to be considered in its original context. The passage you're referring to (at the beginning of The Grey Havens) deals with Sam being busy repairing the damages done to the Shire by Sharkey and his ruffians - such as tearing down the new Shirriff-houses, restoring Bagshot Row etc. To me it's quite clear that the trees were the worst loss and damage only as far as this kind of (reparable) devastation is concerned, and I don't think we're justified in concluding from this that Sam cared more for felled trees than he did for slain hobbits. True, we're not told about his feelings for the victims of the battle of Bywater, and you might argue that this is a flaw. On the other hand, the hobbits at least had a choice and a chance to defend themselves, while trees (outside of Fangorn and maybe the Old Forest) had not.

2.

By offering us an unsympathetic foe Tolkien is able to have his heroes kill thousands of them with impunity & never suffer the inconvenience of having to ask if what they're doing is right, face the possiblity that they have 'sinned', or, most importantly in this context, show them any respect.

Gandalf in The Siege of Gondor to Denethor:

And for me, I pity even his [=Sauron's] slaves.

And Faramir, Gandalf's pupil, in The Window on the West:

I would not snare even an orc with a falsehood.

Also, there is the matter of Éomer dismounting and fighting Uglúk sword to sword at the edge of Fangorn, which has been interpreted on another thread as E. recognizing and honouring valour even in an Orc. Spare hints, but worth considering.
The point, as I see it, is that the heroes of LotR had war forced upon them. The Orcs and other slaves of Sauron's were there, they were attacking the free peoples, and assuming as a given that they were not to be parleyed with (being driven by Sauron's malice), they had to be fought - which doesn't mean that at least some of our heroes (such as Gandalf and those educated by him) didn't regret the necessary killing.

Now to the central question: Should Tolkien have depicted the gruesome side of war more realistically, and how does his failure to do so shape our attitude towards war?
Speaking from personal experience, davem, I have to say that during my first (and second, and third, and probably fourth) reading of LotR, I read the battle scenes very much like you did - sanitized heroicism. Oddly, however, I didn't get the idea from them that war was something good and glorious (actually, I was busy demonstrating for nuclear disarmament and protesting against Pershing-II's at the time). I guess what impressed me most was the fact that it wasn't heroic deeds on the battlefield that won the War of the Ring and saved the world but the sacrifice of a single unarmed hobbit - showing that valour and bravery are not confined to the context of actual warfare.
I think a big part of the problem is inherited from the classic heroic literature that Tolkien was trying to emulate. As far as I remember, we don't see much gore and squalor in the Iliad or the Nibelungenlied, either. The problem, to me, seems to be that T tried to write an epic romance, but in the form of a novel that would appeal to mid or late 20th century readers. Obviously he succeeded to a considerable degree (or we wouldn't be here discussing this), but it may be debatable whether he succeeded completely.
Some modern (=post-Tolkien) fantasy writers have tried to improve on LotR in their depiction of battle-scenes, and I think it's worth the attempt. Robert Jordan, for instance (whatever may be said against him), does a good job at this (as you might expect from a Vietnam veteran), not neglecting the psychological impact of war on his characters, either. (If there are any RJ readers here, I'm thinking of the 'reaction shot' from Perrin's perspective after the battle of Dumai's Wells at the beginning of A Crown of Swords, among many others.) On the other hand, one of my issues with RJ is that while we're getting a fair impression of what his heroes are fighting against, he's not so good at showing us what they are fighting for - no Lothlorien, no White Tower of Ecthelion, no Rivendell, no Tom Bombadil & Goldberry, not even the homely comfort of hobbit life in the Shire.
Which makes me think - maybe Tolkien refused to wallow in the mire of realistic battle-scenes because he felt they would detract from or weaken the impression of the good that was more important to him to describe. On the other hand, the contrast might have made the beauty & glory of Middle-Earth more poignant. But I think it would have been an incredible feat to get both sides right, and maybe we'll just have to accept that our Professor, however much we may admire his achievement, had his limitations as a writer, just like anybody else.