Given that the Spartans in question were Spartan III's, soldiers who began their career as normal grunts like the rest rather than being brought up with the sole purpose of being a super soldier, I'd say that the display of emotion is relevant. And, to be honest, I'd expect a show of emotion from anyone present in such a circusmtance. Reach was a fortress world, perhaps the best defended human world in the galaxy. These defenses protected a significant portion of the infrastructure required to carry on the fight against a genocidal enemy. Without these assets, only a miracle could save the species.
Reach was more than a battle for yet another ball of mud. It was more than just another line in the sand. It represented the only tangible hope humanity had of winning the war. From the Spartans who time and again put down revolts or slowed the advance of the enemy to the ships and weapons of war necessary to continue a war that had already cost the lives of untold billions, Reach was the linchpin of Humanities defensive effort.
So, consider for a moment the crushing weight of the circumstances. Here you face a foe who has rarely tasted defeat, who has brought to bear more personnel and firepower than humanity had yet faced. The formidable defense of Reach put up a hell of a fight and the advance was costly and yet, just when it seemed victory was within their grasp, it was snatched away by the arrival of a second fleet. The ragged defenders could hardly hope to hold out long enough for relief to arrive. Their fleets were shattered, their orbital defenses lay in ruins and the fight on the ground a mere formality as the covenant maneuvered to burn the planet from orbit. The defense was lost, the hope that humanity might somehow prevail in the war was a distant dream. The only thing left to do was retreat yet again.
Here, in the heart of human military might, with all the resources humanity could muster, we once gain stood on the brink of annihilation. The valiant efforts of the remnants of the defenders at least served to allow a significant portion of the population to be saved. It was through the efforts of such men and women, who entered battle knowing they had no hope of victory, that anyone escaped the planet alive. Through a surpreme sacrifice, at least something from Reach was saved.
Yet, even in this dark hour, when the best hope of human salvation lay in ruins, the Spartans stoically continue the battle. City after city has fallen, human strongholds on the planet are folding quickly and, suddenly, a single hope appears, slim though it may be. The covenant came to Reach not to crush humanity - this was simply a convenient diversion. Instead, they came for the information that, thanks to the valiant defensive effort, lay in human hands. It is here that the team is given their final missions. First, they must, at any cost, keep this information out of the hands of the enemy. Second, they must deliver a brilliant scientist to the safety of human lines.
The first job was almost certainly suicide. To deliver the information meant breaching the lines of the enemy that encircled one of the last human strongholds. It meant treading where enemy concentration was thickest and all they had to see them through was a few personal weapons and a battered transport. There could be no delusions at this point: the odds were too long and the mission almost certainly suicidal.
All but one member of Noble team would give their lives in defense of the world. Jorge would die hoping that, by his sacrifice, Reach could be saved. Kat died in the chaos that followed the utter route of a human stronghold. Carter died to allow the remnants of the team the slimmest opening necessary to allow the delivery of the package. Emile and Six died to allow the package to escape.
The price humanity would pay for the loss of Reach would be enormous. Hundreds of ships were lost. Countless divisions were hurled into hopeless battle in the hopes of turning the tide. Millions of civillians were massacred before they could escape. The bulk of the Spartans available to humanity would be lost. In the face of such a defeat, even the most stalwart band of heroes would have to question the merit of standing their ground. Even the boldest would question the merit of throwing themselves into a battle with no hope of victory.
