From what I’ve read, the Norden bombsights were indeed extremely accurate for their day, IF conditions were just right. That includes weather, wind, speed, bombardier skill, everything adjusted just-so from the sight itself, to the bomb racks, altitude indicators, airspeed indicators, bomb manufacturing accuracy, and everything else involved (the Norden actually took over piloting the plane and releasing the bombs).
But all of that was rarely the case in wartime conditions. More importantly, the tactics of the era weren’t really conducive to each bomber sighting the factory and releasing their bombs when their particular bombsight and bombardier did their job. Instead, the realities of anti-fighter defense and issues with accuracy meant that they eventually just ended up with the lead bomber for each group (four squadrons, 48 aircraft) having a bombsight, and the rest kept formation and dropped their bombs when the lead bomber dropped theirs.
Of course, this doesn’t do much for pinpoint accuracy, but it worked well enough for destroying factories and industrial targets like railroad yards. Often the problem was that those targets were in the middle of built up areas, and collateral damage was inevitable.
Combat accuracy was possible- read about the Marienburg raid of 9 October 1943 where 96 B-17s dropped about 218 tons of bombs on the Focke-Wulf plant, putting something like 83% within a 2000 foot radius of the aiming point, which was phenomenal accuracy for the time.
9 October 1943 | This Day in Aviation
But that was accomplished in nearly ideal conditions with little to no opposition. Other raids weren’t nearly so accurate, due to weather like clouds, wind, etc…, enemy opposition/evasive maneuvers, extremely high altitudes, and general slop in the process.
However, even at their most inaccurate, the US bombers were at least trying to hit specific targets, unlike the British who just basically indiscriminately carpet bombed entire cities at night.