Well, relic tried that in apha, cruzz tried that in his mod, I believe both solutions failed.
I believe it mainly failed in his mod because to give Volks MP 40's, he had to use the Grenadier model because Volksgrenadiers have no MP 40 animation, and he didn't like scraping the awesome Volksgrenadier model over them. It failed for Relic because Sturms were very expensive (rectified) and the Raketenwerfer was shit (rectified).
Schrecks on Sturmpioneers and Volks with MP 40's (mirroring Balance Preview Conscript PPSh DPS Curve) and Panzerfausts (possibly cheaper without engine damage crit) could still work, and for historical reasons I'd prefer that. Balance wise we're beyond
needing it though.
They could also make the Special Operations StG unlock apply for Volksgrenadiers as well, except instead of the Obers IR variant, it would use standard version.