The thing is that the best units of Germans were having that attrition, while Soviets were basically throwing away fresh conscripts. That's not a good trade, especially as German resources were more limited than the Soviet ones.
Thing is that's always going to happen because that was an inherent side effects when this German army didn't win quickly. It's pretty much unavoidable so all you really doing is pausing it for a bit. And they know this its one of the driver of the whole go in in quick win quick before you get attrited to death. Which again is all part of the whole German fear of being caught in a long war that they know that can't win and not wanting to get caught in static WW1 type war again. and Honestly even earlier this has been the underpinning of German warfare (or their idealized version of it) since 1871 and what they tried to do in WW1 but failed.
Also, how is not attacking beyond culmination point going to help the Soviets more? By definition, at that point the defenders have the advantage, and as you have said, the Germans had numerical disadvantage. As such, they had to have as good kill ratio as possible.
1). the mistake is think the culmination point is one single point in campaign of this size, it's not the Germans were basically doing it many times throughout the Eastern front (and not just them you see the red army do it during some of their counter attacks as well). That's my point the war is not going to be overturned by one single instance of the German holding off one culmination point for a couple of weeks in Oct 1941
2). any respite in 1941 allows the Soviet to bring up newly mobilized troops and resources, increase defenses and basely recover from the initial shock of Barbarossa that helps them. The Germans know this it why the plan for Barbarossa is what it was
This is trap the Germans find themselves in, continuation past the culmination point too often is costly (and yes probably too costly), but if they dont win quick they lose slow anyway because again time helps the Soviets not the Germans.
War is always calculated risk, the problem is the Germans were using the wrong starting numbers so no matter how good their calculations = "rubbish in - rubbish out"
I wouldn't say that the war was on a knife's edge, as the Soviets could make huge blunders and still win the war. The thing is that the Germans made big blunders as well, but unlike Soviets, they couldn't afford them. So especially with the US not in the fight, I think they have a shot if they manage to avoid those big blunders. But the thing is that a quick victory was a pipedream, and they were forced to the long slog anyways, so they would have had to be really careful not to make costly mistakes.
The thing is the Germany's biggest blunders are made before they even set foot in the USSR and again it's all about the Soviets not the Germans (estimation of strength, will to fight, ability to mobilize, and ability move industry) once they are made they can't be undone once there by the kind of hindsight driven tweaks that come up in these threads.
Another point fog of war is thing assuming anyone is going to run perfect campaign with no errors is unrealistic, and frankly most of the decisions made by the Germans during Barbarossa that often get pointed at were usually made for some good reason even if it goes against our theories for a hinge of war and how they could have won.
And you are right consequently a quick victory is likely a pipe dream, but that still doesn't stop it being their only chance of victory. Which again is why IMO the only way to really change the outcome is with changes with the Soviets not the Germans.
I mean, it's not like the Germans couldn't advance in 1942, after stopping the Soviet counterattacks in the winter which bled the Soviet army white. It took Stalingrad to finally break their back.
The thing is 1942 is still basically more of the same 1941 beat the red army where you find it, try and grab stuff on teh way on the assumption that doing both will cause the soviets to collapse. Only what's the outcome?
The victories are less stunning (but still plenty of soviet casualties) because attrition and difficulty of supply form 1941 - Spring 1942 has had it's effect. And through out the 1942 attacks German forces get weaker and the soviets get stronger, because as above the same underpinning errors are still in effect and time only helps the soviets. Because how do the Germans actaully lose at Stalingrad? Zhukov needs the force there to hold on long enough to buy him time to mass a counter attack large enough to surround and then take 6th army.
Also the 1941-42 winter attacks didn't bleed the Soviet white either? They were costly and poorly executed but the red army is increasing in mobilized size between 1941-1942 (the reach 6.5m in mid 1942 and pretty much stay there for the rest of the war)