In terms of mobility in WWII, I think it must be considered wholistically – Not just in the ETO for 9 months – ie, after Cobra and bocage until hitting the German border in Sept. until after the Bulge in Jan., 1945.

Remember the fighting in Italy was a slog, the Volturno River, Cassino Line, the Gothic Line – Okinawa, the Shuri line and X Corps, Iwo Jima a slog, the Philippines, etc, etc – These are areas where tactical air power and armored mobility leant little to the winning of the fighting.

I believe the reason that Bradley is so charitable toward Hodges in reference to the Huertgen Forest operations is because, in fact, the "fault" does not ultimately lie with Hodges but higher up with Bradley. 1st Army was not obliged to attack the Huertgen, an area that negated every allied advantage. The could have well held their frontage or even bypassed the area and need not worried much about the 5000 odd German troops with little armor and a bad road net counterattacking – in fact it is likely that in bypassing the Huertgen the germans would have simply retreated. In fact, German sources indicate that OKW was confused as to why US forces would attack such an area, with the possible exception of taking the Roer River dams, which US commanders never recognized as an objective until much later in the year.

I think Luke Truxal is far more accurate in suggesting the term "rout" but I would suggest the term "fighting retreat" as an even more accurate of the German activity. The German line was smashed heavily, but rather than being broken and left behind, the Germans were able to pull back and offer significant resistance as they did so. In a true breakthrough, the defenses do NOT pull back. That's the big difference.

As it happened, they pulled their line back towards the southeast, thus attempting to refuse their flank and thereby allowing VIII Corps (NOT Third Army) to advance towards the south. Ultimately, the Germans failed to secure their flank, and the result was that Third Army was eventually able (weeks later) to flank the German forces.

Ultimately, flankings and breakthroughs can have the same long-term strategic outcome in that they result in a deep penetration of the enemy's strategic rear. However, when it comes down to it, I insist that the defenses of Seventh Army were pushed back and flanked, rather than broken through. Its a fairly semantic difference, but it does explain why First Army faced such heavy fighting subsequently.

In fact, if you look at a map, you will see clearly that the geographic region of Cobra was not where the so-called 'breakthrough' army advanced. These were in fact entirely separate operations in two separate regions. VIII Corps did not advance through the Cobra zone, because there wasn't a genuine breakthrough there. VIII Corps advanced to the west, where the Germans had simply withdrawn.

If Cobra had been a breakthrough, you would have seen VII corps conduct a breakthrough attack which would have been followed by VIII Corps advancing through the area already cleared by VII corps. This isn't what happened at all. Instead, VII attacked frontally, forcing the enemy before it to withdraw, and thereby precipitating the rapid withdrawal of the forces before VIII Corps. Once again, if VII Corps had achieved a breakthrough on its own, it would have been able to cut behind the forces facing VIII Corps and upon reaching Coutances it would have trapped the German forces to the north. THIS DID NOT HAPPEN. This was in fact the goal of Cobra, and it was NOT achieved.

The Germans managed to retreat and avoided the danger of a genuine breakthrough.

First Army's operation Cobra resulted in a penetration, the Third Army was the exploitation force.

All of these lines were ultimately broken through in the broadest sense that American units pushed through them. But that is a mis-use of the term. People are looking at a line on a map, and saying, "Well, the Allies passed that line, so therefore they clearly broke through the line." But the term doesn't really apply to a geographic line, but rather to the line formed by an army. In the case of Cobra, the Germans steadily pulled their defensive line steadily backwards in front of the Allied advance. Unfortunately, for them, the geography was such that as they retreated their flank was left wide open. It was this that allowed Allied troops to get behind the German line. Had there been a truly genuine breakthrough, entire German divisions would have been completely surrounded and forced to surrender, and not at Falaise, but at Coutances.

The word 'through' suggests something well in excess of what happened. Even Blumenson makes the mistake of stating that in the aftermath of Cobra the Germans were "impotent". No, I disagree. The Germans did conduct a fighting retreat, which is exactly what a genuine breakthrough is supposed to prevent.

Ultimately, was the effect essentially the same? Sure, by attacking on the flank, Third Army was able to envelop the German flank, but this was only because of geography, not because the German line had ceased to exist. This is why its not a terribly important issue to argue about. But for the troops in First Army, I think it was quite clear that they were pushing a line backwards, rather than having broken through and bypassed that line.