MP isn't happening in 1941, its happening in 1944-45 and the quality of armies shifted towards soviets being better equipped and more experienced then axis despite axis having a handful of heaviest tanks.
Yeah, the red army of 1944 was not the almost shattered force of 1941/42, Operation Bagration proved that. Yet, the soldiers weren't trained nearly as good as the german ones. The goal of the sowjet government was to end the war as quick as possible, no matter the own losses. The soldiers in the shock armies and the guard regiments were veterans from '41/'42, they were elite because they had a high amount of experience on the battlefield, not because of longer training, even though the training methods changed to better.
The Wehrmacht was still better in terms of coordination, troop training and weapons. MG42 or Panther are examples of excellent german weapons.
The sowjets became better, of course, but they didn't turned into soldiers of the same tier as Grenadiers of Panzer Grenadiers.