I certainly agree that the Americans were naive at first, seriously believing Sledgehammer could occur in 1942 or Roundup in 1943 but my sense of the history is that while Overlord was the American Plan C [after Sledgehammer, after Roundup] for northwest Europe, the British agreed to Overlord only with sincere reservations, and the British were giving only lip service [rightly so] to Sledgehammer and Roundup. As far as what to do once ashore, certainly the American plan, turn west into Brittany, was a complete mistake, but thankfully the man commanding Third Army managed to do the right thing after the Cobra breakout regardless of the plan. Absent Third Army's dash east, the Germans might have held Monty indefinitely in Normandy. There is unfortunately no historical precedent for invading Europe from the south. Italy has the problem of the Alps. The Balkans seem inviting, and certainly Churchill thought they were, but that would have put the Anglo-Americans side by side with the Russians rather than squeezing the Germans on two fronts. So, in the end, the right thing was done, thankfully by the UK and the US achieving the proper coordination.
The British never seemed to understand that the main reason Marshall was so insistent on early operations against Germany was because he understood the political savvy of MacArthur and King and the American desire for revenge on Japan could dovetail to derail "Germany First". At the same time he was uninterested in a never-ending peripheral strategy. That was not the "American plan", but the consensus plan of the Allies, which emphasized getting a large port early on - which meant Brest - for the direct shipment of American forces from the Z/I. BTW, it was not Patton who saw the error and the opportunity, it was P. Wood. Patton insisted on following the plan and backed Troy Middleton's decision to drive the 4th AD west according to plan, until Bradley was convinced to turn the emphasis east and push XX Corps and then XII Corps behind the XV Corps spearhead. Unlikely. The German front would have unraveled in late July no matter what. They simply couldn't deal with the rate of attrition they were sustaining. There is also the not so inconvenient problem that I doubt Winnie ever actually looked at a map of the Llujbiana "gap". About the only scheme that was less well thought out was Brookies "strategy" (according to his diary he apparently believed himself the only competent allied strategist) to bring Turkey into the war by attacking Italy, opening up the Dardanelles to allied shipping to the Soviets...mad as a hatter that one was! Working coordination I think would be the better term...I'm not sure it was ever "proper".
The point is the perception of the time. We know now Germany First was 'safe' just like in the summer of 1941 Russia would fall. You base your actions on as much what could happen as you do what might happen.
Were Germans not concentrating their forces to cut the American breakthrouh but the US troops managed to hold the German attack which suddenly led to the panic like German movement out of the Falaise pocket? Also if I recall correctly Hitler himself demanded this attack again and again although it led to massive loss of men and material.