I hate to break it too the party, but the result of just letting the German generals run the campaign with no meddling from Hitler is certainly not the Germans reaching the Urals or even Moscow. Why? Because they might decide to try and go for Moscow in August/September instead of dealing with the rest of the Ukraine.
Despite the claims from various German generals in the post-war, Hitler's decision to halt Army Group Center in favor of reinforcing Army Group South was certainly the correct one. At that point, any further eastward advance by AGC would have broken their logistic train and the Germans would promptly get bogged down against Russian resistance, losing irreplaceable men and machinery for no appreciable gain.
Having the forces wheel south and north, on the other hand, put very little additional pressure on German logistics while also destroying large (if disorganized) Soviet forces on AGC's strategic right flank and denying the Soviets the resources of the industrial Donets Basin. In the mean time, the Germans were able to extend and strengthen their supply lines so they could ultimately conduct IOTLs campaign on Moscow, although not succeed at it, beginning in October.
If the generals have their way, however, the result is an attritional struggle that saps German strength while the Soviets draw upon their greater additional resources (thanks to keeping possesssion of the Donets basin) and those Soviet troops in the Ukraine that were eliminated IOTL get reorganized and a re-equipped.
Come winter, the Germans would be much weaker and the Soviets in a much more favorable position. That could only spell disaster when the Soviet winter counter-offensive kicks off.