Making the Egyptians capable of keeping the Israelis out of the Sinai (and cutting off Gaza even if not entering it), means pretty much everything of the 167 war goes differently. Even if the Egyptians had no troops in Yemen, numbers was not the issue. The average Egyptian soldier was ill trained and motivated and, in common with many Arab (and dictatorship related militaries) generals were picked more for reliability than competence, and rotated frequently to prevent too much "loyalty". The overall competence in technical matters of the Egyptian military was low, and pilot skills were generally low.
All of this needs a fix that would have to start right after the 1956 Suez affair and run counter to lots of realities in a country like Egypt under Nasser.