so its clear that AA guns were not at all successful

I'm not sure that this is so clear. Anti Aircraft Artillery, or AAA, or Flak, or "hate" was a big threat to airplanes throughout WWII. Guns like the famous German 88 were able to take down a four engined bomber with a single hit. If nothing else, such large guns forced level bombers to fly at increased altitudes. If they flew lower, they were subject to a wide variety of more rapidly firing guns--and the reduced time to target made accuracy easier.

Early guns were fired by sight. Later developments added rudimentary radar guidance, making them even more accurate. Making the shells with a timer to explode at a given altitude meant that one didn't even need to score a direct hit to damage an enemy plane. The Allied development of the radio proximity fuse allowed individual shots to explode very near the targeted craft. Initially these fuses were only used over water so that the Axis couldn't reverse-engineer them. The biggest evidence of the effectiveness of AAA is that generally the Germans left the direct defense of the city to artillery--not fighters. Fighters were left to attack on the approach to and the departure from the target. If AAA guns were as ineffective as you claim, they would not have used them in place of fighters for a portion of their defense. Bombers were able to get through to attack, but they suffered debilitating losses--especially in daylight attacks.

A 1945 report from the US Navy on their experience may be illustrative. Even from a pitching deck, AAA was an effective defense. From Chapter II:

Although the burden of ship defense against enemy air attacks fell largely upon our own carrier and land-based aircraft, approximately 7,600-7,800 enemy planes came within shipboard AA. range during the 45 months of the war.

Of these, an estimated 2,773, or 36 percent, were shot down by naval and merchant ships. In addition to these, the enemy expended 314 planes and pilots in suicide crashes on ships.

The Navy gives a total of 2,256 kills from AAA guns. They also cite that many attacks were unsuccessful due to intense fire. Also, on page 10 the report concludes that

[b]ecause of the effectiveness of our day air cover and AA., the enemy began to employ night torpedo attacks early in 1943.

In that same report on page 13, the Navy explains the advantages of the radio proximity fuse (VT fuse in the quote)

These fuzes overcame the major disadvantage of "time" and "contact" fuzes. The value of "time" fuzes has been limited by the necessity of setting fuzes, the inherent variations in time-fuze mechanisms, and the fire-control difficulty of computing range accurately. As an AA. weapon the "contact" fuze also has major disadvantages. Against aircraft a direct hit must be scored before the projectile will detonate, which means that even minor fire-control errors will cause it to miss its target altogether.

As an example of the advantage of using VT fuzes, comparisons have been made of the lethal radius of a 5-inch VT-fuzed projectile and the 40-mm. contact fuzed projectile. A twin-engined bomber in a head-on aspect presents a lethal area of approximately 90 square feet to the 40 mm. To the Mark 53 fuzed projectile, on the other hand, the bomber presents a lethal area of 3,900 square feet. This is figured on a basis of 65 percent operability for the VT fuze.

On page 20, the volume of antiaircraft fire and its ability to dissuade attacks is mentioned.

The volume of ammunition fired per ship-plane action by ships which were attacked but not hit was considerably greater than that fired by ships which were hit, indicating that the volume of ammunition which a ship under attack was able to fire at the plane had a definite effect upon the plane's success.

After WWII, radar-guided guns and rapid firing autocannons made low-level attacks incredibly dangerous. Advances in radar and rocket technologies replaced the high-altitude guns with Surface-to-Air-Missiles. Part of the low-level realm was also replaced with man-portable SAM systems. However, AAA makes low-level attacks quite dangerous.

Overall, AAA may not have been able to keep all aircraft from getting to the target, but they were able to increase the cost of any attack.

(Multiple edits for formatting and content)