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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.