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I have to disagree on most points.
1. I find them more to be a muni sink in a faction that uses a lot of munis for upgrading their troops. In long games it van be an advantage when you are able to pile up muni again, but apart from that I use USF's ATG only when I have to.
2. Barrage is a topic to discuss about, but SOV 6 men crews are mostly alright unless they crew an MG42 or something. Especially to fix the death loop and the fact that you need to recrew them with high RA models.
3. OKW has otherwise no reliable AT apsrt from the Puma that costs quite a lot. If you'd lose fuel control, you would be absolutely screwed as OKW.
4.UKF's team wrapons are almost on par with those of OST. Vickers has okay suppression and decent damage, the ATG is almost a carbon copy of the PaK40.
5. One point that I agree with, but on the other hand you get the best team weapons in the game. So there must be a draw back.
I can't therefore agree with your solutions. This would just make the units even more similar. Currently, every unit has its own feature that sets it at least somewhat apart. Even if your suggestions would solve the rocket arty issue, they would screw big time with faction and infantry/vehicle balance.
When will this myth ever end? The HMG 34 has excellent suppression, only slightly worse than the HMG 42. It suppresses squads within one burst (in ~1.3s at medium range in neutral cover iirc). So does the Vickers by the way, which only struggles when it snipes a model (resetting the burst and thereby halting the suppression) or when the enemy is at max range and in cover.
I think this mostly shows how Rarely people really play the MG34. OKW does not need it for their builds, so people usually skip it. I have the feeling most people build it when they are already losing the whole game. And if it does mot save them, then the MG must be bad because it is associated with losses.