So how does that equate to:
Because at most you're suggesting five "UK" divisions in the entirety of Southwest Asia.
I did say at peak, so aroud eo July 42,
5 Indian, 3 Carpathian Rifle, 6 Indian, 31 Indian Amd, 5 Inf, 56 inf, 8th Indian 10 Indian plus 7 Amd Bde, 10 Indian Motor and All of which are Persia and Iraq command mainly 10 army.
With at an overlapping date, 1, 2 Greek Bde, Free French, 2nd Polish bde, Palestine and 7 Indian Bde in Cyprus, so 8 div, 1 amd 6 Inf Bde.
( technically 10 amd and 26,29 Indian Bde are in Egypt but not part of 8th army) so 9 Divs, 1 amds Bde 8 Inf Bde as part of Middle East Command ( although note Persia Iraq is part split off during the period.) when 8th army consists of 8 Divs.
by Alamein in October the forces in Palestine and X amd are in 8th army but at their peak there are around 10 divs in Middle East command not part of 8th Army. In fact with an near equal army in Iraq/Persia.
Except your "first" wasn't what was suggested; what was suggested were Blamey, Freyberg, etc. questioning the Balkan deployment, raising the issue with their governments, their governments reaching out to the War Cabinet, Churchill having to defend the strategy, etc.
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Well the strategy is to establish air bases on Crete and Lemnos in order to bomb Ploesti and supply a minimal force to the Greeks to assist them vs Italy and eventually prevent the Germans from establishing bases on the Northern Aegean. Don't forget that the Brits had been deployed there since November 1940, so its hardly novel. At the same time Italy has been crushed in East Africa and Tripolitania, being defeated in Albania and driven from the Eastern Med. There is a fair prospect of Italy being knocked out of the war.
Also ofc the strategy includes a pro Allied, or initially neutral Yugoslavia able to block the Struma and the Brits know that Germans are on a clock for any operation in the Med, they know about Aufbau Ost and tracked the movement of armoured forces away from Yugoslavia prior to the pro allied coup. Churchill writes this to Stalin.
The problem is not the Strategy its events. A neutral Yugoslavia blocks ( its terms of the tripartite pact with Hitler) access to Greece. A pro allied but mobilised Yugoslavia forces germany into a head on offensive against the Metaxis line while the Italians are being pushed back. Its the speed of the German reaction and success of the invasion of Yugoslavia which makes it fail, none of which can be known in late march when the deployment begins.
Any complaint by a division commander about the strategy ( which is a big deal, Division commanders are supposed to obey orders) has to rest on the strategy being wrong in planning not in execution.
And you have to ask what is the alternative. Sit in Tripolitania or continue the advance to the Borders of Vichy North Africa at a time when the planning or the Invasion of Syria is advanced. Rashid Ali after the failed coup in Iraq controls the Syrian/Iraq border and Syria is within a few miles of the oil pipeline to Haifa which supplies the entire med theatre.
This is a complex fast moving situation. An Alternative is the Yugoslavs do mobilise in time ( i.e. the Germans delay) the Left flank of the Metaxis line is secured, Italy knocked out of the war and a large part of Army Group South not available and a shaky Romania.