The allies had a hilarious advantage over the germans in pretty much every intelligence gathering method possible. At times, they had a significantly better picture about the german side of the front then the german high command itself. They used this to a devastating degree already once shortly before D-Day, when in their operation to destroy the Luftwaffe in France they read every message of the germans, where they discussed how hard the allied hit them and what they hoped they wouldn't do because they had a couple weakpoints they assumed the allies didn't know about..cue massive attacks exploiting those.
So even if one accepts your narrative about the famously weak-willed wallies who throw the towel the second they have less then 100% success ( a popular narrative, including in the german and japanese commands of the time, but pretty wrong) then "don't know how bad the germans are reeling" is just about the last possible reason to rattle them.
The Germans were notoriously bad at intelligence operations (partly because they were incompetent and partly due to deliberate sabotage) and indeed the allies (both Russian and Wallies) were much better at it. Most famously through Ultra intercepts. But that didn't make them all-knowing, not by a long shot. They often got things wrong. I suggest you actually read up on Normandy. That campaign alone shows numerous oversights and plain mistakes, even overlooking entire German divisions. Nothing for them to lose the war over but certainly not fool-proof. Both the counter-attack at Salerno and the Battle of the Bulge were intelligence failures. Or perhaps more accurately intelligence analysis failures.
I have never said the Wallies were weak-willed. But as democracies, they wouldn't or couldn't accept casualty levels authoritarian states did. Not after WWI which still had a strong influence on western societies. So massive casualties with no progress IMO would indeed rattle the Wallies. I'd expect a change in commanders (much like Churchill replaced commanders in North Africa) and (eventually) a change in strategy.
As to the Wallies not knowing if the Germans are reeling or not, this is not unique to them. It was difficult for all combatants to really know what the state of the enemy was. After the breakout in Normandy and the rout of the Germans, the allies believed the Germans were finished. Instead, they started recovering almost immediately and even before Market-Garden, they were putting up a stiff fight again. And you can't rely on German intercepts because units often misrepresent their losses. IIRC, the 9th SS Panzer Division administratively "disabled" vehicles to keep them from being handed over to the 10th SS Panzer Division before Market-Garden.