That's true but you still have fausts, schrecks, and raketenwerfers to cover the luchs, and not having stgs might lead to some more interesting combined arms play with the kubel and Sturm's dealin the main portion of damage along with the luchs. And double brens/bars usually take a pretty long time to come out, by which time you will probably have obers to do some stomping of their own. However, I definitely think your solutions could work too. Right now they're just far too spammable/cost effective and versatile for the faction they are in.
You're completely right with regards to how supported the luchs could be, and that I probably understated how effective the luchs is when allied light tanks come out.
Arguing that not having stgs could lead to combined arms play is pretty far off though. Kubels are only useful for capping and their vet 1 ability after 6ish minutes, which is probably the time/phase of the game were referring to (since thats probably when volks first start getting stgs). They really don't contribute that much dps, especially when squads on both sides are vetted.
As for sturms, its not as simple as having volks be "meatshields" and sturms as "damage dealers." In a 1v1, sturms can usually win in most situations against rifles and even penals. But in a 2v2 with light cover on both sides, with 1 volks squad and 1 sturm squad vs 2 penals or 2 rifles, the volks and sturms would lose pretty hard. Part of it is that rifles and penals are stronger than volks (vet0, no upgrades either side, of course) so im not adding equal units to both sides, but its mostly because of how focus fire works. The sturms can sit with the volks at max range, but then the allied side wins because sturms dont have as much long range dps. The sturms can charge and make use of their excellent close range dps, but then theyre crossing open cover against two squads in cover and get melted, after which point its 2 allied squads vs one axis squad. The tl;dr of it is that sturms do worse the larger engagements are; they do best in 1v1s. This means that this unit performs well individually and does terribly in combined arms.
For a more technical explanation of the above: the volks are sitting at max range, so they are using their max range accuracies and max range cool downs; theyre not contributing that much damage to the fight. When the sturms charge they get better accuracy, better cooldown, longer bursts, etc. but thats not enough because theyre closing in on and being shot at by two squads. These two allied squads get to take advantage of their decent close range dps. This means you have two allied squads doing their close range dps, but only one axis squad doing its close range dps with another doing its long range dps.
You could get both axis squads to charge, but then the sturms still get melted and have to retreat since theyre crossing open cover, meaning that the volks may make it across with full health, but then theyre facing two full health (more or less) allied squads that both have a better dps curve for close range. The situation doesn't change much even when the volks have stgs unless they also severely outvet the enemy.
Finally, the volks can throw a flamenade at the allied squads while the sturms charge, but if the sturms charge, they still get melted and have to retreat; the allied squads no longer have cover, but then its 2v1. If the sturms dont charge, then the allied squads can back away for ~10 seconds, and the axis player loses 30 munitions, after which the allied squads can go back to that piece of cover; its a resource win for the allied player. There are quite a few things that can go wrong in the flame nade situation that pushes the engagement pretty hard in the axis players' favor, but again, I think we can all agree that flame nades need at least some kind of change.