Quite an elementary arguement, sorry to say.

Remember, how the Germans used the StuG in WWII would be very different vs how they could be used in AH2. It offers *nothing* that the current Pzr4 cant do better.
You mentiojned "battlefield survivability"... stop and think just how quickly our current line up gets knocked out. I mentioned the M18 because it offers something we dont cuurently have: high speed, medium gun (better than current Pzr4, less than 17lb'er), and low armor (but better than M8). The M18 would be able to stand up vs the auto ack better than the M8, but not much else above it. It isnt designed to stand and fight, it is designed to shoot-n-move. I could see a JgdPzr IV being used as a legit TD in this game, but even then it would be handicapped.
The StuG would get owned in this AH2 game. Stop and think how often one can sit and only traverse their main gun 15d and do anything worth while. To start up the engine to turn the tank 45d or 90d to get a shot would be suicide. I try and mix up what tanks I tank in the game, and if the StuG would be introduced it would be considered a Pzr4 without a turrent. Would you take a Typhoon or La7 up and only use %50 of its throttle? No... why do you think anyone else would do the same in a Pzr4 vs StuG choice?
You mentioned the Sherman vs Churchill vs StuG???? and you picked the StuG??? There are far more perameters to think about than just for me to be able to blurt out "this one!" as a preference. Each of those tanks did something better than the other and the StuG was the most limited, imo.
The problem with the 2 American choices is battlefield survivability. they would be no better than the current firefly. The stug was in fact the most important piece of armor to the German army. It was basically the back bone of both infantry and panzer divisions . To say it did nothing well is not correct. If I were a tanker and my choice was a Sherman , Churchill or Stug I would go Stug everytime. The Tigers turret traverse is very slow and starting it's engines rather than wait for the barrel to go around 180deg makes more sense to me, besides in lw TT where this would be used there are engine noises coming from everywhere so what's the big deal about leaving your engine running. You could use this thing to sit in the trees concealed and fire from standoff range where it's limited barrel traverse would be just fine. I'm sure that some of the games best tankers would find a use for it and be quite deadly with it.