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In conclusion, if in your opinion Soviet need an CP 0 assault squad suggest that instead of asking to move the PPsh to CP 0. That would make both unit easier to balance.
Since I'm not motivated anymore atm to give an answer to all the small aspects you commented I'll focus on your conclusion since you gave one (although I disagree in all of them but the last and would have quite a few remarks).
About your conclusion:
No, I'm not of the opinion that Soviet needs doctrinal 0 CP Assault troops, but neither USF, UKF or Ostheer really need one. Because of that all of them are doctrinal, for different openings with different commanders and versatile playstyle.
Yes, Imo the PPsH Cons upgrade is rather underwhelming at its timing at 2 CPs in comparison to the timing of other assault options at soviets themselves or other factions.
So either rework its timing, bundle it with another conscript upgrade or completely exchange for another commander ability. Replace it in Soviet Shock army for sure (since Schock army should keep Schock Troops).