S!
Ok I've checked the records, and the average height would be around 25,000, not 23,000. But that's still not 30-35,000.
Plus Bomb Groups were comprised of 3 Squadrons which flew in "box" formations which spaced the squadrons at 1,000 foot levels. The low Squadron was 3,000 feet below the top one.
Here are some sample heights:
44th Bomber Group, Dec. 20th '42, Rominy, France: 23,000.
91st BG, Jan. 27th '43, Bremen, Germany, 25,000.
44th BG, Feb. 15th '43, Dunkirk, France, 20,000.
93rd BG, Feb. 26th, Bremen, 26,000.
100th BG, Oct. 10th '43, Bremen, 24,000.
366th BG, Feb. 8th '44, Frankfurt, Germany, 24,000.
93th BG, 4th March '44, Berlin, 28,000.
96th BG, 18th June '44, Bremen, 25,000.
379th BG, 20th June '44, Munich, 25,000.
44th BG, 13th Aug. '44, Rouen, France, 18,000.
96th BG, 2nd Nov. '44, Meresberg, Germany, 24,000.
385th BG, 21st Nov. '44, Wetzer, Germany, 25,000.
The examples presented above fit into this pattern.
It seems that the very heavily defended targets like Berlin were bombed from higher altitudes. However this came with a penalty.
An anecdote on cold:
Al Greenburg, 96th BG on a mission flown at 30,000 feet on Nov. 9th '44:
"The cold at altitude was terrific... The bomb bay doors wouldn't close electrically and the pilot was having a fit. He couldn't keep his airspeed up. Finally after 15 minutes, the engineer cranked them up... The trouble was, that at 30,000 feet, half the devices which worked on the ground wouldn't function."
Accuracy:
The much vaunted Norden Bombsight was supposed to be able to drop a bomb "in a pickle barrel from 20,000". In fact it was much less accurate.
Hal Turrel, Bombardier, 445th BG;
"After dropping a few bombs, I no longer subscribed to the much advertised 'pickel barrel' theory... our practice bombing was done from 5,000 feet with 100 lb practice bombs which were filled with sand and had a smoke bomb which went off on impact so we could see where we hit. I did not think I was very good... I gave some thought to the fact that in combat we would probably bomb from 20,000 feet which would reduce our accuracy quite a bit."
The USAAF eventually trained its crews to aim to hit within a thousand foot circle.
Charles MaCauley, 385th BG on a mission over Berlin:
"At the Rally point we looked back and saw the target exploding in flames. We had scored direct hits. Nearly all our Squadron's bombs had landed in the thousand foot 'bulls-eye' circle."
Most of the time, a group's bombs did not have such accuracy.
Even when bombs hit the targets, they didn't always do as much damage as the USAAF believed.
For example on Oct 14th 1943, approx. 260 B17's hit Schweinfurt's ball bearing factory.
The USAAF Bomber commander for the mission, General Frederick Anderson, described the results as: "...entire works inactive... may be possible to recover 25% of production."
In fact the actual result was 3.5% of the machinery of the factory destroyed, and 6.5% damaged.
Overclaiming by the Bomber gunners was also very apparent on the mission. Gunners claimed 199 German Fighters shot down. Actual captured German records showed 38 Fighters destroyed.
60 bombers were lost on this, the most costly of USAAF missions.