Turn three, Dolittle claims its Messina and Reggio Calabria and not so much the Luftwaffe casting their malign influence down the East Coast of Sicily and seeks permission to take them out with his heavies. Alexander refuses, too much flak. Flak=losses. Alexander plays the long game here, priority repairs in Siracusa and Catania should help nulify the threat and presently all the supply is coming over the Southern beaches and ports and he is fighting a low intensity campaign which all being well is not taxing on supply. Manuever should bring Messina.
I would side with General Doolittle here.
Reducing ports reduces the flow of supplies, and reduces the ability to stockpile supplies, this has the effect of increases enemy losses and reduces your own. Lost freight also equals lost equipment in a reduction from production pools to simulate the destruction of replacement stocks amongst the freight. IF supplies can't flow, then replacements cannot be received. Supplies are the lifeblood, and draining your opponents blood from the start is a good strategy. Refusing to do so in order to save your airplanes for WWIII is a mistake. Just watch your production and adjust your mission rate to keep losses below that. Time is not on your side.
In short: Doolittle wants to kill Krauts and break their war machine, and it will have the added bonus of reducing the naval interdiction on the ports you intend to count on for supply that are currently blockaded by naval interdiction.
A week's bombing by 4-6 bomber groups in an air directive covering both ports should shut them down for as long as you'll need to capture Sicily. Use the Recon Fortresses to observe your damage. With P-38 escorts everyone should get through and flying over the target at 21,000ft I haven't seen bad flak loss. Have you changed the settings in any of the air doctrines from default?
At the start of turn 5 I'm showing:
That is flak losses that are <15% of my total losses, and I'm flying my bombers out to destroy ports and rail all the way up to Salerno and Bari. But this is against the AI
Not sure what the lost Axis air frames are. Be careful of putting too much stock in numbers that might be largely Italian at this point. You'll see high operational Axis losses due to automatic naval patrol by the Italians.
In my same game, at the start of turn 5, 36% of 1028 Axis air losses are Italian.