There may have been some debate about the plight of the Third Army, but it isn’t really one in which the sides are equally regarded. The vast majority of experts at the time and afterwards were in no doubt: a modern army surrounded in the desert, cut off from any hope of resupply, and now subject to uncontested airpower of its enemy is in deep, deep trouble. Most sources simply state that it was political motives, not military ones, that prevented its complete destruction - if it was war to the knife, they would have been annihilated.
Apparently, this was the Egyptian Commander’s contention, and he ought to know. From the same Wiki article:
Saad el-Shazly was the Egyptian Chief of Staff during the war … if he said “the fate of the Egyptian Third Army was in the hands of Israel”, I’m inclined to believe him, particularly where it accords with common strategic sense. It is highly unusual for an army in its position to successfully break out of encirclement (at least, as an intact army, capable of fighting again).
As for the peace deal - again, it is worth pointing out that the barrier to a deal was on the Egyptian side, not the Israeli: Egypt had signed on to the “Three Nos”, when Israel was willing to trade the Sinai after 1967. The war was, from a rational POV, pointless. The main thing it accomplished was assuaging Egyptian military pride (they had lost, undoubtedly, but ‘with honour’ this time, as opposed to the one-sided humiliation inflicted by their military leaders in 1967).
As for Soviet Military intervention, they were unwilling to risk it in the face of American threats, allegedly.