Well, they must have some anti-tank weapon. Although Soviet doctrine always claimed the best anti-tank weapon is a tank, there are situations when you can use infantry, but not tanks. Soviet had big airborne force and they needed RPGs or something similar for their paras.
I know, you just started shouthing: they had BMDs (airborne version of BMP, infantry combat vehicle)! True, but imagine a situation - you are a Soviet para, your unit just captured a bridge in some West German town, now you have to defend it. Unfortunately, your BMDs have problems with manouvering in streets. German counterattack has no such problems - their tanks can smash building together with your soldiers sitting inside. And your men can not do nothing! RPG is cheap and quite efficient way to multiply your anti-tank firepower. Not to mention the fact, that RPGs are good to destroy bunkers, fortified houses etc.
Frankly, I do not think any serious infantry after WW2 would give up an idea of a light, man-portable antitank weapon, especially after Panzerfausts and Bazookas. Sorry, but what you propose is simply imposible.