[Boromir88]

At first I thought this thread was an attack on our own Boromir 88, & was going to jump to his defence, but then I thought, Nah, actually he does have quite freaky motives most of the time.....

The valiant davem always looking after others and looking for his own glory therein. (That sounds sort of familiar and I'll get to it in a bit), but first.

Thinlomien:

Was Boromir really so important to Gondor's army that it would have been indeed stupid to send him away, as I have said?

Boromir is called the "Captain-General," in today's terms that would be like the Commander in Chief role. He would be the head of the army commanding it, not simply a figure head. In the US one of the presidents roles is to be the Commander in Chief of the armed forces, since he already has a lot of jobs and surely can't do everything by himself there are of course people there to help him and make decisions. However, the President is the head hancho of the army and can tell troops where to go. Also if we look at Rohan Theodred was the leader of Rohan's army. It seems custom to have the son and heir be the leader of your forces. So I woud say he was an important tool to the army.

Looking at Boromir's point of view, I still can't see why did he want to go himself.

Well let's see what Boromir has to tell us about receiving this dream:

"In this evil hour I have come on an errand over many dangerous leagues to Elrond: a hundred and tend days I have journeyed all alone. But I do not seek allies in war. The might of Elrond is in wisdom not in words. For it is said. I come to ask for counsel and the unravelling of hard words. For on the eve of the sudden assault a dream came to my brother in a troubled sleep; and afterwards a like dream came of to him again, and once to me.
In that dream I thought the eastern sky grew dark and there was a growing thunder, but in the West a pale light lingered, and out of it I heard a voice, remote but clear, crying:

Seek for the Sword that was broken:
In Imladris it dwells;
There shall be Counsels taken
Stronger than Morgul-spells.
Ther shall be shown a token
That Doom is near at hand,
For Isildur's Bane shall waken,
And the Halfling forth shall stand.

Of these words we could understand little, and we spoke to our father, Denethor, Lord of Minas Tirith, wise in the lore of Gondor. This only would he say, that Imladris was of old the name among the Elves of a far northern dale, where Elrond the Halfelven dwelt, greatest of lore-masters. Therefor my brother, seeing how desperate was our need, was eager to heed the dream and seek for Imladris; but since the way was full of doubt and danger, I took the journey upon myself. Loth was my father to give me leave, and long have I wandered by roads forgotten, seeking the house of Elrond, of which many had heard, but few knew where it lay."~The Council of Elrond

So, it seems from this that Boromir felt the road was doubtful and dangerous and that he should go (showing his pride and protectiveness for his brother). And Denethor reluctantly agreed to let him go.

I think Boromir was needed in Gondor, but the reason Denethor and the elders let him go was because he just wouldn't give up and insisted upon going. As Faramir told us his brother would not be stayed. So, Denethor reluctantly let Boromir go on this journey to Rivendell, fully expecting that he would return, however their time was pressing as Sauron as attacking.

Now, why would Boromir feel the need to go and put himself forward. It's probably a combination of things:
1) He felt the road was dangerous therefor his brother should stay behind and he would go.

2) Faramir tells us:

I could well believe that Boromir, the proud the fearless, often rash, ever anxious for the victory of Minas Tirith (and his own glory therein), might desire such a thing and be allured by it....~The Window on the West

Perhaps Boromir felt like Rivendell held answers as to how to save Gondor and he would go being "anxious" for it's victory and his glory.

I think those are the reasons why Boromir felt like he needed to go. And the reason that Denethor and the elders let him go was because he insisted to go and wouldn't have accepted anyone else going "he would not be stayed..."

Formendacil:

What state was Boromir's military reputation in?

I love speculating as well, there's a sort of freedom experienced by the reader to come up with their own ideas and thoughts. (Which Tolkien wanted to do and why he refused allegories). He wanted his readers to develop their own opinions about his books and sort of let them grow and change. But on this speculation of anti-Boromir and Denethor, I would have to disagree with you.

As far as Boromir's military reputation I think he was absolutely fine. Eventhough he did lose the recent battle they were far outnumbered and what ended up beating them was the Witch-King's presence. But, I doubt there was blame placed on Boromir for losing, as we are told the men loved him and here's probably why:

"Some said that it could be seen, like a great black horsemen, a dark shadow under the moon. Wherever he came a madness filled our foes, but fear fell on our boldest, so that horse and man gave way and fled. Only a remnant of our eastern force came back, destroying the last bridge that still stood amid the ruins of Osgiliath.
I was in the company that held the bridge, until it was cast down behind us. Four only were saved by swimming: my brother and myself and two others. But still we fight on, holding all the west shores of the Anduin; and those who shelter behind us give us praise, if ever they hear our name: much praise but little help. Only from Rohan now will any men ride to us when we call."~The Council of Elrond

It's very important to troops to have their leader fighting alongside them. It's an inspirational feeling and above that he fought until the absolute last minute when defeat was iminent...being one of the last men to escape. So, I despite the loss I still think he was adored and praised by the men.

As far as Denethor goes, considering people still listen to him when he's lost his mind and says burn me and my son, I would think also that he had the respect from his City. I'm sure had he been alive and resisted Aragorn's claim he wouldn't have had a lot of support especially after Aragorn proves himself. But, he proved himself very capable of leading Gondor until he foolishly believed he could be Sauron and his mind was litterally overthrown.