The MP 43 - StG 44 is not a rifle...It's an assault rifle comparable to the AK-47 and was used as such.
The notion that the troops did not use the MP 44 on full auto as a standard tactic(suppressing fire etc) stems from it's early combat testing,initial combat use. Not due to a defect in the weapon but form a lack of magazines and an adequate way for the single man to carrying enough mags during an assault.
By '44 magazines were in adequate supply for the amount of weapons issued and a ammo harness to carry the mags was in use.