The United States is obviously at war in that Farmboy match which is why his units can come to Africa and Gibraltar. Germany built only ground units which is the common G1 strat now as they can reach Bryansk on the G5 which is very pivotal part of the game, forcing Russia to turtle in Moscow for the mid-game. Over-spending on German navy is a common mistake of novice players and one of the main reasons why people fail to consistently win as the Axis in OOB matches.
Italy could have gone to Syria on I1, but getting that nice Greece/Southern France bonus is wonderful for their economy. I usually find that Italian forces in Iraq get quickly overwhelmed by the British without too significant of casualties. Planes can hit it easily from Egpyt and India making the location difficult to defend in the early game. Personally, I like using the transports to take Cyprus and Malta which are expensive for the British to reclaim without losing transport/ground units themselves and is a major drain on the UK production until the mid-game. I am not saying your idea is bad, I just haven’t seen it successful enough to make much of an impact.
The Adam-Farmboy match is Balance mod so there are additional incentives for both Axis and Allies to hold the islands in the med.