Right, and in the Med it was an ongoing debate between the Luftwaffe and the ground forces, and between the bomber pilots and the fighter pilots (notably JG 27). The bomber pilots wanted closer escort, and distrust between fighter and for example stuka units led to the latter being very quick to jettison bombs and emit smoke and go into various escape maneuvers as soon as they saw Allied fighters, much to the dismay of ground forces (who sometimes had 'friendly' bombs dropped on them). There were heated debates in the Luftwaffe about this.
Fighter pilots liked to attack the Allied fighters in the safest possible way, picking them off from above (preferably when they weren't paying attention) and quickly disengaging / evading. This worked very well to quickly accumulate very high scores for a handful of experten. But when it came down to either attacking of protecting bombers, including breaking up attacks against their own airfields, these tactics didn't succeed so well.
This was a major factor after the reorganization of Allied Air forces in mid 1942 and notably, at El Alamein. It is in part what lead to the destruction of J.G. 27 and their replacement by J.G. 77 in fall 1942.