Massive...
Handwavery ahead. 1) Say the Axis is able to take Egypt in 1942 and is able to reach the Suez, would they be able to launch a Middle East campaign? 2) Would the Arab population rise up in Palestine and/or Iraq? 3) Would Axis paratroopers already in North Africa be able to use bases in Egypt to drop on the other side of the Suez in Palestine and achieve something or would they get slaughtered? 4) At this point there is no Jewish brigade, that didn't happen until 1944, but the Palmach, the military arm of Haganah was officially raised by the British in mid-1941, roughly 1 year before Egypt was threatened in 1942, so they would be a factor, depending on whether the Arabs rise up against the British, then they might be forced just to defend their communities.
5) What would the US do? Would they still pull Torch or would they have to reinforce the Middle East directly and preclude landings in North Africa?
Massive...handwavery, that is.
Minor problems:
A) The Quattara position was an excellent defensive position that could not flanked, even if the Axis had unlimited supplies and a troop differential sufficient enough to break up the 8th Army - which they didn't.
B) Then there's the Nile and C) the Delta - both equally excellent defensive positions.
D) Then there's the Canal itself. Yet another.
E) Then there's the Sinai. Yet another.
F) And there are the 9th and 10th armies, aka PAI Force, including what amounts (in 1942) to a half dozen British, Indian, and Polish divisions.
It's the reverse equivalent of the Italian campaign, except the Axis forces, supply lines, and general quality are light years below what the Allies deployed in the MTO in 1942-45.
Other than that, it's a great plan.
Questions:
1) No. As the Israelis and Egyptians both showed repeatedly, the Suez Canal is an excellent anti-tank obstacle (So is the Nile, but you didn't even mention the river, so there you go);
2) No. In Palestine and Jordan the Arabs actually provided enough volunteers for a substantial enough force the British could raise what amounted to a motorized infantry brigade from them; in Iraq, they'd already tried it and been destroyed by an expeditionary force of what amounted to one infantry division and a partly motorized/partly horsed cavalry division, and the loyal Iraqis (Assyrians and Kurds, largely);
3) No. This is after Crete. Think von der Heydte's "brigade" during the Ardennes - except they are trying a daylight drop.
4) True. Wingate was already in India, but given the need, he could be in the Middle East in a day or two, so there's a British general officer ready to work with the Zionists and who will be accepted by them.
5) TORCH goes forward, if anything with more of a priority, since it is the obvious riposte to any Axis success in eastern Africa; it amounts to a second front, using the Allied superiority at sea and in combined operations to do just that...
Best,