I am fine with allied infantry being better than axis infantry, its part of the 'balance of power' in this game. Provided I can reasonably beat or push back their Inf with some other mechanic. Normally that would be the axis MG42 dealing suppression and knocking part of the enemy force out of the fight, allowing your weaker grens to fend off the remaining force. The counter play here is that if you fuck up with your HMG they can win that fight.
The problem is currently that Light tanks and the mortar remove the ability for Ost to properly use this mechanic. Thus if we fix the mortar and light tank play (which would also require fixing the rest of the call in meta to keep things balanced) we can again properly use this mg cat and mouse system to beat riflemen.
Now i agree that the double lmg rifles are too strong but with a small situational nerf like slowing them down you force the USF player to use them with more care and be smarter about where they place them. A slow blob means the opponent can take the rest of the map. It would also give more time for the mg to move and to suppress and make them highly flankable.
Given that rifles are pretty much the only inf unit USF has (non-doc) and other units tend to be very expensive and not too viable and axis having non-doc elite infantry on hand (obers and pgrens), having them limited to one bar or one lmg would, i think force USF into a do or die attack for an early game win because they would have no ability to win a late game infantry fight. Nor do USF have much ability to win a late game tank fight.
The main source of imbalance comes from light tanks and the mortar, double lmg rifles should be toned down but not crippled.
Also RE's shouldn't be able to equip any weapons apart from maybe a zook.
That completely ignores the fact that (if we have it your way) Riflemen still hold all the answers US needs in a single unit, while any other faction has to diversify their army and thus limiting their field presence. This goes especially of Axis HMGs, as they are significantly less mobile than their Allied counterparts, except for the Vickers.
Light vehicle play actually isn't a big problem here (aside from perhaps the double 222 issue and the T-70, both of which could easily be fixed with cost adjustments), because it arises from the USF mortar, which allows for a way too early Stuart. Adjust the mortar, and the Stuart will come out at a proper time, allowing opponents to properly prepare.
The LMG issue on the other hand exists not only for a certain part of the game, it basically pops up as soon as USF gains access to LMGs. A single BAR already performs well enough to let Riflemen do their job, while a second one is simply overkill. If you were to adjust that "slightly", the change wouldn't be strong enough, while a large nerf would make many USF players (rightfully) wonder why they would have to pay for twice for effective equipment.
P.S.: I also fail to see why Rear Echelons shouldn't equip anything but a single Bazooka. If we follow that thought process, we should simply remove weapon racks and implement Bazookas as a RE only upgrade and BARs as a Rifleman upgrade, but then Relic could just generally stop doing asymmetric balance...