1st method - comparing exchange ratios and attrition.
The base assumption here is that to defeat the European Axis, its enemies had to inflict at the least the same combat deaths on Axis forces as the Axis sustained in OTL, as part of rendering Axis forces completely incapable of resistance through conventional combat (this exercise excludes the atomic weapons factor).
I used casualty figures from Wikipedia to establish the German (actually the entire European Axis) KIA exchange ratios with the Soviets on the one hand and the western Allies, respectively, to estimate the likely sacrifices required by the Soviets to defeat the Germans without the western Allies, and of the Western Allies to defeat the Germans without the Soviets –
WWII Military casualties (from Wikipedia, illustrated in text and chart)
Eastern Front (European Theater) OTL –
Axis – 5.2 million
Soviets & clients – 10.65 million
Exchange ratio – 2.05 Russians per Axis
Western Front (European Theater) OTL –
Axis - .8 million
Western Allies (& Yugoslavia) – 1.5 million
Exchange ratio- 1.9 western Allies per Axis
The figures aggregate the Yugoslavs (probably conventional forces and partisans) with the western Allies, and I suspect that the Yugoslavs had a much worse exchange ratio with the Germans than the British Commonwealth and American forces had, distorting the exchange ratio to make it appear worse for the western Allies. So, I’ve added two different alternatives for the Western Front trying to exclude the Yugoslav factor
Yugoslav casualties were .45 million, suppose they were responsible for .05 m (50,000 Germans)
…Exchange ratio 1.4 western Allies per Axis
Suppose Yugoslavs accounted for 100 k, or .1 million
Then exchange ratio (exclusive of Yugoslavs) would be 1.5 western Allies per Axis
If the Soviets had to fight the Germans to the finish without the Western Allies, we might reasonably assume that to bring about German defeat, the Soviets would have had to face and kill the number of Axis military forces that the western Allies faced and killed.
So, that would have been another .8 million (800,000) Axis troops the Soviets would have had to kill.
At the prevailing Axis: Soviet exchange ratio, 1 : 2.05, this would have caused 1.64 million additional Soviet military deaths. And by the measures already used it would have led to a wartime total 12.29 million Soviet deaths, a figure 15% higher than OTL. Did the Soviets have the manpower reserves and political capacity to recruit, train and expend another 1.64 million soldiers?
This seems within the realm of the achievable, although accounts often mention the Soviets hitting the bottom of their barrel of manpower reserves by 1944.
Playing this in reverse, if the western Allies had to fight the Germans to the finish without the Soviets, we might reasonably assume that to bring about German defeat, the western Allies would have had to face and kill the number of Axis military forces that the Soviets faced and killed.
So, that would have been another 5.2 million Axis troops the western allies would have had to kill.
At the prevailing Axis: Western allied exchange ratio, figured at 1 : 1.4 (the best-case), this would have caused 7.28 million additional western Allied military deaths. And by the measures already used it would have led to a wartime total 8.33 million western Allied deaths, 793% higher than OTL. Did the Soviets have the manpower reserves and political to recruit, train and expend another 1.64 million soldiers? Using the 1:15 exchange ratio the western Allied situation worsens to 7.8 million additional deaths , and using the 1.9 ratio it worsens much more to 9.88 million additional deaths.
This seems within the realm of physically achievable given the populations of the US, Commonwealth, Empire and (plus a probably available Latin American manpower pool that they could access more easily than the Axis or Soviets). However, it would still be hard, given that unlike most Soviet manpower, the North American center of gravity of these manpower reserves is across the ocean, and manpower needs to be allocated to production and maintenance of equipment for long-distance heavy transport as well as for firepower and mobility in range of the battlefield.
Sustaining combat effective forces to make up for Soviet non-participation would have been a staggering effort physically. Politically, it is hard to imagine it succeeding, and even if it did, the consequences to the western Allied societies would have been immense and would have dwarfed the consequences of WWI.
The western Allies have the further problem of having to attack over the sea, enabling only small initial fronts that would need to be widened, against Axis forces capable of reinforcing defenses in depth and counter-attacking to far greater degrees than in OTL.
The 2nd method calculates the cost by the number of KIA the Soviets sustained per mile of advance toward Germany and thenumber of the KIA the western Allies sustained.
This method makes things appear relatively better for the western Allies, compared to the previous method, although still horrific compared to OTL. And it makes the task confronting the Soviets much, much harder, to the point of daunting.
First the Soviet situation -
1,350 miles from Stalingrad to the Elbe –
Soviets lost 10.65 million fighting men to advance this distance
At this rate, .007890 million (or, about 7,890) were lost for each mile of advance
Assuming no western Allied attacks in Europe, the Soviets would have had to cover an additional 700 miles to reach the Atlantic coast of France at Brittany, or 795 miles to reach the French-Spanish border.
Based on the Soviets historic cost in military deaths per mile, this would have resulted in an additional 5,523,000 military deaths to reach Brittany (or, by analogy, 6,272,550 to reach the Pyrenees) –
..so half again as many losses on the Soviet side as OTL, pretty doubtful.
Now, for the western Allies
558 miles from Normandy to the Elbe -
Western Allies lost 1.05 million fighting men to advance this distance
At this rate, .001882 million (or about 1,882) were lost for each mile of advance
Assuming no Soviet participation in the war as an attacker or defender, the Allies would have had to cover an additional 467 miles to reach the eastern boundary of German occupied Poland. Based on the western Allies historic cost in military deaths per mile, 878,894 more western Allied service people would have been killed getting there.