The bombers suffered a ridiculously high casualty rate, were easy prey to enemy fighters, and made little difference in ground engagements. It was the soldiers of the Heer who won Germany's early battles, not the Luftewaffe.
So what if the Luftewaffe were restricted to only making fighters for the entire war?
There are a few examples where bombers made an impact early in the war:
- Warsaw: the city was surrounded and surrendered after being bombed heavily. But a surrounded city is doomed anyway, so the absence of bombers just leads to a delay.
- Norway: This was principally an air invasion. So the absence of transports (yes, not even mass transports in this ATL) would mean Germany could not invade Norway. So potentially Germany is stuck using lower grade iron ore the rest of the war (more on that here: viewtopic.php?f=76&t=243663)
- Fort Eben Emael: Okay, a few transports for a small elite force of Fallschirmjäger will be necessary.
- Rotterdam: The Dutch were already negotiating a surrender, so the bombing of Rotterdam didn't really matter.
- Sedan: The supposed crowning achievement of the Luftewaffe as a tactical bomber force, the 1000+ sorties flown by the Luftewaffe killed a whopping 56 French soldiers (source: Lloyd Clark, Blitzkrieg, Myth and Reality. The money would have been better spent on just about anything else.
- Barbarossa: The Luftewaffe destroyed most of the Red Air Force on the ground in the opening week of the invasion ... except the Red Air Force was back up and running by late summer and in many sectors had air superiority. But the Heer was still able to win. Air forces simply weren't that effective on the battlefield in 1941. And more fighters would have better protected the Heer.
This would also save Germany a ton of resources and manpower. The Luftewaffe was a tremendous drain on the resources of the Reich (40% of the armaments budget, 1.8 million laborers by 1941 and more aluminum than the Reich could produce). Fighters are far cheaper than bombers. This would have freed up men, material and factories for the Heer, which never received enough equipment during the war.
And the biggest advantage would be late war - the focus on fighters would mean the Luftewaffe would at least be better prepared than in the OTL for the Allied air onslaught that wiped out the Luftewaffe from 1944-1945. There would be more trained fighter pilots, more efficiency in producing fighters, more technological research and expertise put into fighters, and more institutional experience in running a fighter based air force.