Okay so I'm going to make an assumption here, that when you're talking about "Allies" you mean the Western Allies, not counting the Soviet Union even though they were very much one of the Allied nations.

The main reason the allies didn't use captured German equipment is fairly simple. There was no need. The German Tiger I/II's were difficult to deal with in a straight up engagement but there were never very many of them and there was rarely a need to engage them head on.

Germany only fielded about 1500 Tiger I/II's throughout the entire war and only a small portion of those were in the WTO. The bulk of the German Panzer divisions were Panzer IV's and Panthers and the allies didn't really struggle with those. In fact, the Sherman was generally superior to German Medium tanks in most regards. It is faster, more maneuverable, has a higher rate of fire, better sight stabilization, quicker turret traverse and offers better visibility. The German counterparts may have thicker frontal armor and sometimes bigger guns but that doesn't matter nearly as much as people think.

On paper, if a Sherman and a Panther were to stand in an open field and slug it out, odds would favour the Panther but why would the Sherman ever do that? The allied advantage in basically everything (near total air superiority, mobility, supply, artillery, numbers etc) allowed them to pick their engagements more often than not and on the defensive the Shermans took out German medium tanks at a rate of 3,6:1. In the interest of fairness, on the defensive the German medium tanks will also take out Shermans at a rate of 3,5:1. In either case, only the Tiger I/II's are difficult for a Sherman to deal with, particularly earlier models, later models could very well pierce even the frontal armor of a Tiger with standard AP rounds.

All that said, there are many other ways to kill a big cat. Tank destroyers, of which the allies had plenty, can hadily deal with a Tiger. CAS, of which the allies also had plenty, can also easily dispatch a Tiger. Artillery, of which the allies had literally more than they knew what to do with, can also kill a cat. In a pinch, even determined infantry can deal with a Tiger, particularly at close range.

Added to this Germany was dealing with problems of their own and many heavy tanks were simply abandonned due to a lack of supply or mechanical failures that could not be rectified in the field. So, what few Tigers there were did not pose a significant problem for the allies and so there was little need to try to use captured enemy equipment. Had tigers been a major issue the Pershing did exist and could have been deployed to Europe in much larger numbers, certainly enough to match the German Tiger numbers. However, General McNair saw no need to do so because adding Pershings, or captured enemy tanks, would have stretched the already troublesome allied supply lines even further. McNair, who was an artilleryman by background, prefered to deal with Tiger I/II's with the means on hand and in retrospect I find it hard to fault him for that.

Sourced primarily from "Data on W.W. II tank engagements involving the U.S. Third and Fourth Armored divisions" by David Hardison, US Army Ballistics Research Lab and "The Infantry's Armor: The U.S. Army's Separate Tank Battalions in World War II" by Harry Yeide.

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!