your other points are important to note and are valid, however  > yes, there were death camps they weren't death camps. they were slave labor camps. any extermination that occurred was 1) largely outside of germany, and 2) almost entirely during military campaigns. people weren't killed in the camps, they were murdered less than a mile from their homes and dumped into graves in unmarked locations. or simply killed during a "combat maneuver" and brushed under the records as being war casualties. the deaths in the camps were from starvation (ironically as a result of allied bombing as others have mentioned) and from disease. millions of people did not die in the camps, the logistics of that quickly become a ludicrous fantasy if you start crunching the numbers. the millions of claimed deaths occurred outside the camps with no official records of the bodies.
United States