Everything U wrote is true and I totally agree.
The "problem" is not that great. Generally, looking at tourneys (1v1/2v2) and analyzing matches one thing can be said for certain. It is easier to play as allies than axis. The difference is nowhere near what it used to be (thanks to the balance team - great bunch of people still making sure that the game experience of many players is better than in the past).
Pzgrens with shrecks are just one tiny example of small "problems" that add up with other small "problems" creating small but significant imbalance. The key is simply that the better penetration and dmg don't offset slower reload, worse far range accuracy, more manpower that has to be invested in the squad that holds pzshreck, more mp to reinforce, and the fact that the have less hp than larger squads. One also needs to add the fact that this is the only stock squad that can wield hand held at on the ost side. Allies can equip hand held at on many other squads and don't need to sacrifice more expensive squads. If they do sacrifice them, their at performance is boosted by the relatively new "elite" bazooka performance. The idea is probably to just adjust pzrshreck performance a little bit, so that the result of a relatively big resource investment into a shrecked elite squad is more predictable/reliable. We're probably talking of small differcences. Just look into sander vs jibberjabberjobber discussion in the thread on Sander's personal balance changes.
OP is right - for an elite and glass cannon squad they seem to miss too much. I'd suggest a blend of both solutions. Make them be more accurate from the start with less damage and instead of receiving better accuracy with vet, they should deal more damage with vet instead, so that at vet 3 their damage output is similar to what it is now.
Them having lower hp and a longer reload and have chance to miss more at long range (esp vs lights) is couteracted by fireing the first shot fastest, having higher damage, higher pen while for the most part they face lower armour values.
Schrecked pgrens have high alpha damage potential but low rof, this makes them less effective vs lights, but thats usualy 1 or 2 units per game. But the high pen and damage keeps them more relevant as the game drags on. Them missing imo is less frequent vs bigger armour.
Here standard hh at from allies begin to fall short. Mainly cuz of lower damage and pen while these do much better vs lights cuz of higher rof and better acc af long range.
As for not having to sacrifice expensive squads to become at squad. Only soviets have a simaler squad next to their main line. Usf only have rifles early on, rear echelons are pretty weak and putting bars on them is not very efficient imo. Putting zooks on them is however. The officiers can do it too but as far as i know limited to 1 squad of each.
Super zooks from rangers have no baring on the possible imbalance of shrecked grens. They are limited to 2 commanders if i remember correctly. And you also give up their amazing ai power.