Unternehmung Wacht am Rhein was a desparate gamble, and probably shortened the War by a year. If the War had dragged on, Germany, rather than Japan, would have been the recipient of the first nuclear attack. It was just that much easier to destroy German Armor in the open. All of Germany's reserves of ammunition and fuel were expended in a month.
In August 1944, the Wehrmacht suffered more fatalities than the Americans did in the entire war, mostly on the Eastern Front, but the western Allies kept the Germans tied down trying to keep them out of Germany.
The US Army took more casualties AFTER December 26th pushing the Germans out of the ‘bulge’ created by their initial push. The correct solution for the allies would have been to “pinch off” and encircle the German Armies. Instead Eisenhower decided to just “push the air out of the German balloon”. German soldiers were simply abandoning their equipment and walking home. Most of their tanks and transportation simply ran out of gas.
Eisenhower was back to playing “Broad Front” strategy after the Brits failed to get into the Rhur Valley in “Operation Market Garden”. Ike had a very tough job holding the alliance together and he obviously thought that he couldn’t too many chips on the table in any single hand.