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At the same time you get your first lmg42 you also get your first pzgrenadier which is completely capable of pushing anything 1:1 the USF player can oppose, after all that's an elite unit.
Now we can't take the Gren vs riflemen matchup in a vacuum, there is also the HMG42 and pioneer with super vision to articulate your early game.
So yes, I don't see any particular reason for Ostheer to not push only with infantry.
Since i said that, i think you responded to my post. Let me answer back. From my experience at least.
Hipothetically: (not the same as vacuum experiment)
Lmg42 is a heavy investment that competes with teller mines, one is needed in case LVs come into place and the other to keep riflemen away. If the OST player used the munition on one,
he will not be able to react to the other Pgren are effective but really MP heavy and also bleed more than grens, its anoter way to keep AI potential, at the expense of MP instead of Muni. In both cases (LMG, pgren) the usf is a step ahead in the reaction chain and probably seeing the OST player strategy clearly, if its a defensive or pushing unit composition. Pgren can be beaten by brute force that USF can handle. On the other side, OST is "forced" to
open its strategy(namely, show it, make desitions that will exclude other options aswell), because grens succumb among riflemen if no other route is taken, therefore losing map control and probably the game. Pgren might be the best tool OST has to break the stalemate.
Offensive openings dont involve HMG42 simply because of its vulnerability and even when they force a single squad retreat,in 1v1s the map is open enough to allow flanks or cutoff maneuvers. If you are not flanking the MG, it means it is idle and thats one squad less for OST (260 MP to be exact) that is already losing in 1:1 encounters.
P.S.
In all situation we are representing a typical match that has OST and USF going for the OP premise. A medium tank rush, with the needed tools in between.
Therefore, if a map is garrison heavy, grenades and ambo are required, even when OST dont invest in FU for their tools, they are not having the upper hand vs early USF. BP1 is quite easy to achieve, but then BP2 is the hard part, the part that USF exploits the most. If OST goes for LVs then the example is broken, if USF goes for LVs, the same thing.