Why not? The Regia Aeronautica's standard tactics is bombing from altitude by level bombers - largely unsuccessful.
The Germans may deploy Stukas to Sicily. But these will be B Stukas, not the Ds that sank british warships in 1941. Compare the two versions and you'll see that they are really two different aircraft, not to mention the lack of anti-naval training in 1940.
The Royal Navy only has to carry out a couple of fleet raids to wreck the attempt on Malta. People seem to assume that once there are a handful of paratroopers there, the battle is over and the Axis won't need to send in supplies in the old-fashioned way.
You seem not to understand BB armor and what a mission kill is. The Axis does not have to sink the ships, they just have to damage them enough to force them to retire. Now if dropped from more than about 1000 feet, an HE bomb always defeats the weather deck. The weather deck has to be this thin (1" or maybe up to about 2") due to ship design issues. A thicker deck will make the ship too top heavy, make it more vulnerable to BB main gun fire, and make it just plan old too heavy/slow.
Now lets think about what happens to a BB. They sink for one of two main reasons. They take on enough water to where their weight exceeds the water they are displacing. Mostly an issue for torpedoes and mines but I am sure you can find cruiser or capital ships that sink from flooding only cause by bombs. The other reason they sink is due to losing the main powder/ammo magazine. A lot of the design of BB guns and armor relates to this issue. An AP shell will explode about 42 feet into a ship if not stopped by armor. This is deep enough that the 100 or so pounds of HE is likely to be near a magazine and therefore sink the ship. So when we get a gun/bomb that can consistently penetrate this deep, each shot is likely to catastrophically end the life of the ship, and you will be hard pressed to find many ships that survived 4 main gun explosions 40 feet or so into the ships. This is what the armor of a ship is designed to defeat, naval gun fire at a narrow range of angles.
Now airplanes cause huge issues. If we start getting 2000 pound or larger AP hits, we just start losing battleships. But fortunately for many BB crewmen in WW2, many times they are attacked by either HE bombs or smaller AP bombs. HE bombs dropped from low altitude (say under 1000 feet) will often explode on the weather deck. Some of the energy will penetrate the deck, but most will be wasted. There is a small chance of still getting a catastrophic loss, but not a huge chance. Some chance of major damage, but not critical. Now even if the ship is lucky, a ship that takes repeated hits from HE bombs (say 10) of 250 lbs to 1000 lbs will almost certainly have a dry dock cycle coming up.
Now the problem becomes when AP bombs are used, which will happen if you stay off the coast too long. While at the right range (invulnerability zone), an WW2 BB can take a 2000 pound AP hit and take very light damage, a much smaller AP bomb cause huge issues. Why? The naval shell is hitting 12" to 15" harden armor plate. The AP bomb is hitting a 1" weather deck and say a 6" deeper armor deck. It can have more velocity. And the key is the bursting charge (50 to 100 pounds) is taking place deep in the ship, where it is will be very damaging and is likely the find a main or secondary magazine or boiler spaces.
So yes, a BB can often shrug off a few hits of smaller bombs. But in most cases, even light damage cause issues. Each time you are hit, you will lose crew men and guns and equipment. The cumulative effect of this small hits over a week or so on station will always be the same. Either the ship is sunk or a drydock repair cycle.
So all that happens in you scenario is the UK is trading cruisers and capital ships for a few planes, bombs, and fuel. A huge German win. So this is why it is pretty clear that when the attack on Malta begins, the RN will be the better part of a week away, and the Germans can get ashore.