Hmm, this does lend itself to a possible alternative - Stop after Vyazma/Bryansk are pocketed, reduce the pockets, and see what you can do down south with the freed-up supplies; the Soviets need to rebuild the central front anyhow since you're already too close to Moscow to ignore.
Perhaps, but in that stage of the war the Germans were not keen on such opportunistic moves. They wanted decisive, spectacular and radical solutions to Germany's fundamental strategic problem: Germany's isolation in a part of the Eurasian continent poor on the natural resources needed to carry on a protracted war against a world coalition.
Then there were other problems of a more practical nature. The month's pause of AGC after the battle of Smolensk did not lend itself to much rebuilding of its forces. Initially, AGC had to
Panzergruppen (later renamed as Panzer Armies), nos. 3rd (Hoth's) in the north and 2nd (Guderian's) in the south. These two
Panzergruppen, being the spearpoint of the German offensive, had seen constant fighting since June 22. They had conducted the encirclements at Minsk and Bialystok against the Soviet western front, and later (the first nasty surprise of the campaign for the Germans) another encirclement against the undetected forces of the Soviet second strategic echelon immediately west of Smolensk. At Smolensk,
Panzerguppen 3 and 2 had to hold the encircled Soviet forces on their own until the 2nd, 4th and 9th Armies arrived (by means of constant forced marching) to relieve them partly of the task. And not only did they need to fight the Soviet forces trapped within the Smolensk pocket, because (in the second nasty surprise of the campaign for the Germans), the Soviets formed three more Fronts (Western, Bryansk and Reserve) east of Smolensk and hammered at the German armored ring from outside.
After these fights, the two
Panzergruppen were exhausted, but even when Hitler decreed the general pause for AGC, these two
Panzergruppen were not allowed any rest;
Panzergruppe 3 had to execute a gruelling march north to join Leeb's vanguards approaching Leningrad (a march more than 400 km first north and then south to rejoin AGC, made on the vehicle's own tracks and wheels, through marshy and wooded terrain) and Guderian was redirected south and subordinated to Rundstedt's AGS, so he had to conduct yet another enciclement; with a fighting advance that took him 400 km south and then back.
Meanwhile, the Soviet Western, Bryansk and Reserve Fronts kept hammering at the German 2nd, 4th and 9th Armies with decreasing success, leaving them extremely weakened (the main reason for the staggering initial success of Typhoon) until the STAVKA called the attacks off.
When finally Halder managed to convince Hitler to launch the final attack on Moscow, AGC was only "relatively" rested and recovered. Most of September, the infantry had been repelling Soviet attacks, although in well entrenched positions and with relatively light losses. But the German logistical services had been unable to restore a proper supply line to AGC; whatever supplies arrived during these weeks were just enough to enable AGC to defend itself from the Soviet continued attacks, and so it was extremely difficult to build up even modest supply dumps behind German lines to support further advances.
But even worse was the situation of the (newly renamed) Panzer Armies, 2nd, 3rd and 4th (until then subordinated to Leeb's AGN, but now sent by Hitler and the OKH to reinforce AGC). The three Panzer Armies had seen constant combat since June 22, without any proper pause to repair damaged vehicles, and without receiving proper reinforcements.
This was a serious setback for the Germans, because the success of their tactics depended entirely on their mobile forces; as they'd been fighting non-stop since day one, and had no time to rest and had received no reinforcements, they were now seriously weakened.
By October 2, the day Typhoon was launched, Guderian's 2nd Panzer Army had only in active duty 25% of its authorized vehicle strength, and some
Panzergrenadieren regiments and motorized divisions were also seriously depleted in manpower. Hoepner's 4th Panzer Army and Reinhardt's (replacing Hoth) 3rd Panzer Army were in a somewhat better shape, but they both hovered around 50% of their authorized vehicle numbers in service. As for the state of their mobile infantry forces, the same stands as for Guderian's army.
It's true that the Soviets in front of AGC were in even worst shape (the result of their continuous attacks for almost two months), but the Soviets were receiving a continuous flow of replacements and putting new forces in the field, while the Germans were not. Time had been running against the Germans since June 22, but by October, it was running even quicker against them.
It's worth noticing again the poor performance of German intelligence. As usual, the Germans had good intelligence of the forces immediately in front of them, which allowed them to conduct the initial attack with such success. But any further than that, and they were in the most absolute darkness. The Mozhaisk line was a complete surprise, as were the forces that Zhukov scrambled together to cover it, and again it was another complete surprise when the Soviets pulled out even more fresh troops for their December counterattack.