I think the Germans should have stayed out the Med entirely just proping up Italy within that country.

On Malta the problem the Germans had was one of their own making. They were actually quite good at supressing the island when they tried. The problem was that once they did supress it they let up and Malta recovered, once again becoming a thorn in Germany's side.
This pattern was repeated at least three times by the Germans. Part of the reason this occured was that Germany really lacked the economic base to produce sufficent aircraft and fuel to maintain an aerial siege against Malta. Invading Malta was likely beyond German / Italian capacity. The British rapidly reinforced the Island to a point where anything short of an Allied style amphibious assault would have certainly failed.
In a sustained assault by aircraft alone the Germans would have had to commit several hundred bombers and crews along with a similar number of fighters on a prolonged basis to keep the island subdued. After all, the British were pretty regularly sending 50+ new fighters to defend it. With attrition the Germans would have had to be willing to lose potentially hundreds of aircraft to accomplish their goal. The Allies could affort such losses. The Germans couldn't. In fact, they couldn't muster aircraft in the numbers required to make such a campaign work without severly hurting their operations elsewhere.
Malta simply was not worth the sustained effort.