I think AA overall (not just for OKW) feels like an unfinished mechanic. It doesn't feel consistent enough nor does it feel rewarding if you actually focus on AA units. It kinda feels like something they put in but never bothered to finish establishing but thought 'yeah that's good enough'.
What someone said earlier about there being a 5% chance to actually shoot down the plane without their being any health makes so much sense. That's exactly what it feels like - imo it really shouldn't be this.
This is actually one place were what you described is pretty historically accurate.
The AA given to ground troops was pretty inadequate for the job. The range on many of the AA guns was no more than 1-2 miles at best. A gunner had to use iron sights to track and lead a plane moving at 250-350 miles per hour. If it is heading right for you the speed and deflection is less of a problem, but you are also shooting at it for a pretty short time.
The answer was to mass the amount of firepower. It wasn't one 50 cal gun that would bring down a plane, but having dozens trying to do so with the hope that some might find the target.
That said, there are other elements that are less historical. Allied ground forces were MUCH less likely to be exposed to air attack or recon than Axis ground forces. Not just were there more allied aircraft, they didn't have to spend time defending their own cities or lines and were able to keep the Luftwaffe on the defensive. It was pretty rare by 1944 that the Luftwaffe was able to play much of a role at all.
Further, the Allied planes were much better suited to ground attack. Sturmoviks and Typhoons were designed for ground attack, and the huge P47 was a heavily armored, fast, and very durable plane that turned out to be really well suited to ground attack. (One US P47 pilot, Robert Johnson, tangled with a bunch of German planes returning from an escort mission. He and his ground crew counted some 20 20mm hits to his plane and lost count of 7.62 hits when they were into the hundreds.)