That's debatable. Initially, a lot of the territory that the Arabs advanced into were not held by Israelis. And of course, it wasn't too long before the Israelis significantly outnumbered the Arab armies. Compare that to the Yom Kippur war, where the Israelis lost a significant chunk of their tank forces in the first few days, and felt the (somewhat overblown) fear that Syrian forces may have broken through.
The difference is that in 1948 both Syria and Jordan were able to hold small strips of territory from what was to be the Jewish state, and only lost them in 1967 with the Golan and the west bank. In Yom Kippur the Syrians were pushed back and lost even more land, while Egypt lost some on the Western bank of the Suez and had it's gains to the south encircled by Israeli forces, and the 2nd army to the north was not in a position to defend it's gains had the war continued.
How exactly am I wrong there? You admitted that the Egyptians assessed that taking the whole of the Sinai was highly unlikely, but go on to criticize the limited approach of the Egyptian High Command in their plan. I pray you consider the fact that if the Egyptian forces had advanced further into the Sinai, they would have lost their SAM cover which was crucial for neutralizing Israeli air superiority, but would have also lost cohesion which would have made an Israeli counter-attack more successful.
The problem is that Egypt treated the Bar-Lev line as the actual defensive line, and thought that taking that would mean victory. The line was made of look-outs and was to be the early warning for the mobile defense of the Siani, which was to come from three passes through the Sinai. Egypt knew this and thought it could delay the Israeli forces by sending heliborn commandos with ATGMs. It didn't work out, since like I said, the plan was so full of holes that while the Egyptian army was to be protected by the SAM shield, the helicopters had little protection. Those who did not die while being shot down, did so when the Israeli forces pretty much went through them. Out of ~2,000 commandos sent in the first 2 days of the war, nearly all were killed or captured (I think over 730 KIA, I'll look it up later), with the longest delay I can recal was ~25 minutes when an Egyptian company got destoryed (~70 KIA IIRC) while trying to delay the 162nd div.
The Egyptians were not wrong to think they can't take more, they were wrong that they can just take little and hold it.
As for the working plan, the initial part of the plan certainly worked. The Bar-Lev line was taken, significant Israeli forces were destroyed and the initial counter-offensives had been beaten back relatively easily. The Egyptian High Command had made extra contingencies for the plan (Phases 2 and 3) but the evidence points towards them never taking these seriously.
The first stage called for five beach-heads with a 10km radius, that will later link up for a 10km deep strip. The transition from stage 1a to 1b is the problem here. While Egypt thought that it worked, in actual fact it didn't. There was link up between the two beach-heads to the south, and the three to the north, but nothing between. This is due to the Israeli forces defending on the first two days. Problem is the actions of the Israeli high command, where Gonen shares most of the blame IMHO (but I think that is for another debate), that resulted in the attack on te 8th looking like it did, and to the garrisons of the Bar-Lev line to remain there to be captured. It means nothing regarding the Egyptian position, since that was proved to be faulty when the Israeli crossing encircled the 3rd army. Same forces, same setting, just a more orgenized Israeli offensive.
This is simply nonsense. The Egyptians unquestionably had the upper hand in the first few days of the war. Unless of course you are arguing that Israel was destined to win the war anyway.
Without a major POD (or even a series of PODs) before the war, no, there was no way for Egypt to win. After one reads the descriptions of the battles of the first days of the war, it becomes apparent that the whole thing was a matter of time. The Egyptian beach-heads were not "swept away" (like was the prevailing beliefe in the Israeli high command), but they were also prevented from succeeding in thier intended mission. The problem is that generaly, everything looked like it was going according to plan, minus a few "setbacks" for the first couple of days. In reality one can see the causes for the Egyptian defeat were being planted in the first hours of the war. Namely the failure of the armies to link up, the failure of the air force to destroy Israeli HQ and intelligence instalations, air bases, with jets on the ground a la "Six day war", the failure of special forces to delay the Israeli reinforcements, the failure of the navies to cancel the threat of the Israeli navy or an Israeli amphibious landing, the failure to cancel the Israeli armored force with the use of ATGMs and tanks (I know, 402 tanks destroyed and all. Though that figure is worthless by itself. It cost more then five (5) times that number for both Egypt and Syria, together with more special forces and other AT carrying infantry then Israel lost soldiers in the Six day war, the War of attrition and the Yom Kippur war combined. And the Israeli armored force was still able to repair and place over 400 captured tanks, bringing it back to where is started the war with).
I'm not quite sure what you mean here. When the Egyptians embarked on phase 2 of the offensive (which as I mentioned before, the actual military High Command did not want to go through with), it was in response to a Syrian plea for help.
When Political leaders interfere with military operations, their interference's tend not to have the best results. Even those with military experience like Sadat. And I've previously discussed, Egypt was hardly doomed to defeat from the very beginning, so your defense of Sadat on the grounds that the war was already lost is rather confusing to say the least.
The thing is that the Egyptian high command thought is had succeeded with stage 1, and wanted to play bunker. Sadat either wanted to help Syria and/or retake as much of the Sinai without it being presented to him that Egypt cannot hold what it has, let alone try and take more. He thought that it was possible. Still, we agree that it was a bad move. We just disagree on it's importence, since I claim that it had little impact on the results of the war (unless we look at things from the humanist perspective, and say that a few hundred Egyptians might still be alive).
Many of the sources I've read on the October war tend to paint Egypt's goals as being rather limited, aiming at the crossing of the Suez canal, the defeat of the defending Israeli forces on the other side and the defeat of the Israeli counter offensives. And of course, until the 14th, those objectives were all going quite well.
Disregarding the sources (I've seen the official war goals, which are so limited one can say even a large operation from the War of attrition could fulfill them, and I've seen maps that show the finale goal is deep into the Sinai, so I'll leave that for now), that's 2 out of 3. The crossing and the victory over the Bar-Lev line were mostly achieved, but they were dependant on the Israeli counter offensives to fail to be determined a success. The counter-offensive on the 8th was a failure, but the crossing on the 15th would have happened either way, and the reasons for it's success were established on the first day.
The Egyptians did try to counter-attack the Israeli penetration at Tasa made during Chinese farm, but the Israeli use of TOW missiles, as well as Sadat's refusal to consider moving some Armoured forces on the East bank of the canal for use anywhere else ensured that the Egyptians did not have enough forces available locally to have a good chance of actually doing closing the gap, so to speak. The intensity of the Egyptian counter-attack at Tasa actually took some Israeli commanders aback OTL, who's to say it is doomed to failure if the Egyptians have more forces available and are more willing to use them?
Fist of all there were no TOWs by then, the first one was fired two days after the cease-fire and IIRC achieved no hits due to the Egyptian use of simple wire fences infront of thier tanks.
Regarding Sadat, I doubt moving forces the the west bank of the Suez would have helped, considering the logistics going with that it would probably not be fast enough, and even if it was somewhat successful, it either leaves the 3rd army incapable of defending itself, or it means that "Green Light" happens and the same result happens. But now you bring up another POD, where not only is Sadat not giving the order to attack on the 14th, but also he does not give the order to stay on the east bank. Are we discussing the OP, or trying to figure a plausible scenario for an Egyptian victory?