I covered this aspect of the issue in my first post albeit in a more simplistic manner. Effectiveness of a bombing mission is a function of both bomb tonnage and accuracy. The USAAF (and Allies more generally) tended to forget about the second part. It's great if your aircraft can carry 8,000 lbs of bombs, but if they all land 3,000 to 30,000 ft away from the target, then the amount of bombs really doesn't help at all. The USAAF conducted a lot of studies during the war and in roughly the next decade after the war which subsequent research proved to be deeply flawed. In part this was political (see "Bomber Mafia") and in part due to lack of an accurate understanding of the enemy records.
There are some military or Strategic targets for which very large bombs (like sub pens) or vast quantities of bombs (like say, rail yards) are needed. For most targets of military importance however, accuracy is really far more important. Not that many things can withstand a direct hit from even a 500 lb GP bomb. But even a 2,000 lb bomb or a gigantic 10,000 lb bomb will have very little effect on the target if it hits over the next hill. The US spent a vast fortune on the sophisticated gyrostabilized Norden bomb site, which was supposed to make high altitude level bombing sufficiently accurate to hit a "pickle barrel from 30,000 ft" to paraphrase the propaganda. But that was only true in tests done under ideal conditions. And conditions in the field were never ideal. In the early war bombers were often unable to even navigate to the correct city let alone pinpoint the radar station or a fuel depot. It was only after the adoption of things like radio wave direction finders that navigation (particularly at night) became comparatively reliable.
Hitting targets in Central Europe where the weather was rarely clear and sunny with still air like some test range in Nevada, and never so convenient due to aggressive fighter attacks and efficient flak concentrations, proved to be well nigh impossible. Yes you did have to send mission after mission out to try to knock out that ball bearing factory, not because of a lack of bombs (there were more than enough by an order of magnitude), but due to the abysmal level of bombing accuracy. We know from post-war analysis that while some quite important targets were hit (I don't know how far they could have gotten with it but I'm very glad Heavy water research facilities were taken out for example) most German industrial production in particular was relatively unaffected by Allied Strategic bombing.
This is in part why planners made the (IMO quite dubious) decision to shift to "de-housing" as the euphemism went. If it was that hard to hit an individual factory or rail yard, then send a ton more bombers and just flatten the entire city. Well this killed and made homeless millions of civilians, destroyed priceless architectural landmarks, art, archives and so on, it did very little to further the actual war mission. It certainly didn't cause a morale collapse in Britain, Germany, or even Japan in spite of the horrific level of firebombing there. This continues post-war. The vast amount of bombs dropped on North Korea didn't win us the war, it just mad the enemy into extra crazy underground dwelling trogladytes. We moved massive amounts of mud in Vietnam, but that didn't dissuade the Viet Cong, nor did it ever stop the flow of supplies on the Ho Chi Minh trail. It just left a vast minefield of unexploded ordinance along the borderlands in Vietnam, Laos and Cambodia.
You raise a reasonable point about flak. For defense against flak guns are useless. You basically have speed and altitude for defense, and to some extent elaborate maneuvering and course changes such as which were worked out by the 8th AF and Bomber Command etc. later in the war. In some Theaters, for example in the late War against Japan, flak was really the only risk, as fighter defense became negligible. However over Germany fighter defense was a substantial problem for bombers almost to the end of the war, including incidentally at night, where Bomber Command found that casualty rates began steadily increasing as German night fighters became more and more effective.
Aside from that, you are basically talking aboe about Strategic bombing. Lets not forget that bombing missions also included Operational level bombing and Tactical bombing, all of which was also quite important. In fact considering that the only real Strategic target of merit turned out to basically be oil fields, arguably Operational and Tactical bombing was actually more important. And if you look at the operational histories from places like North Africa and Russia, not to mention the Pacific Theater, heavy defensive armament was indeed quite important.
For example, from MAW III and IV it's very clear that the majority of German and Italian aircraft destroyed during Allied raids on their airfields were taken out by Medium and Heavy bombers, all quite heavily armed types. Older categories of bombers (pre-war designs) struggled to survive in that Tactical environment in spite of having fairly heavy escorts. The Tactical impact of fighter bombers and dive bombers was also reported by ground commanders to be significant or decisive in numerous battles.
