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I think you are making a bit of a mistake in classifying infantry into 2 types ('basic' and 'elite') and saying that because Grens are basic infantry, they should lose to / be worse than elite infantry. The way I see it, that model only really applies to OKW and Soviets, and even then only to a certain degree. Ostheer has no elite infantry (i.e. infantry built from late-tier buildings that start out very strong), but Grenadiers become your elite infantry with the LMG upgrade and sufficient veterancy. Just because Guards are 'elite' doesn't mean you can directly compare them to Grens - all units have their role.
To deal with your 'examples' in a general way, I'd like the point out the Guards are intended as a dual AI/AT unit, decent DPS against vehicles and the very useful 'button' ability. This is a good chunk of what you are paying for with the manpower cost and DP upgrade. Grens have no AT except the Panzerfaust. Cons are obviously weaker than Grens, but have far more utility with Oorah!, AT nades, Molotovs and various other Doctrinal abilities. Shocks are a close range unit - they will absolutely tear through Grens if they get near (and they have smoke grenades to do this). Obviously 1 Shock unit will lose to 3-4 Grens, but unless you are heavily outnumbered Shocks will more than pull their weight in close-quarter situations. There are also other factors to consider here: Grens have no means to clear buildings, and their 4 man squads leaves them very vulnerable to being squad-wiped by a demo charge, artillery round or lucky grenade.
Now, let me say that I actually agree with you that these matchups are often too one-sided in the favour of the Grens. However, I think that is an issue with Soviet units being too weak, not Grens being too strong. I think Shocks are fine, but Cons need some sort of buff to make them useful, and Guards need to drop their weapons less at the very least.
The reason why I think this needs to be fixed on the Soviet side is that if LMGs were much weaker, I believe there would be a kind of tipping point where Ostheer would suddenly become pretty much unplayable. Ostruppen strats aside, as Ost your Grens are the workhorse of your army throughout the game. If Grens with LMGs couldn't beat Allied infantry in the way that they currently do, it would be trivial to overwhelm them with things like Cons or Penals, which would break the entire faction.