No, the bombing effort was not a failure. But the greatest payoff of the effort had its beginnings with the invasion planners redirecting of the efforts of the 8th and 15th Air Forces to targets they thought would make the Normandy landing easier. Once the thinking of the air bosses got channeled in that direction, by late summer 1944, the importance of attacking oil began to have the priority it deserved.
So, this is a series of stepping stones. First, you need enough control of the skies to make bombing something other than suicidal. Second, the Soviet front in the East has to envelope the Balkan oil fields. Third, somebody had to arrive at the idea that the German Army might be pressed for fuel if the refineries and synthetic plants were bombed. Now, finally, you have arrived at the most important target for the bombers.
And yes, the British participated in this effort to, if begrudgingly. Sir Arthur Harris said, "I still do not think that it was reasonable, at that time, to expect that the [oil] campaign would succeed; what the Allied strategists did was to bet on an outsider, and it happened to win the race." This is probably true but what matters is that it worked.
In getting back to the subject of this thread, yes Italy should have been invaded simply because the pieces were not yet in place to mount an invasion in the North.