It's a scoped rifle, and it has several /wildly/ different dps profiles depending on the squad using it. The STG should be the weapon to act as you describe, the G43 really should be a mid/long range focused weapon, not a "close range/On the move" armament.
Well the Semi-Automatic Rifle profile came first, with the Jaeger Light Infantry Upgrade for Grenadiers and Panzergrenadiers, the G43 upgrade for Panzerfusuliers, and the Jaeger Light Infantry Recon squad which was equipped entirely with G43's. The G43 DMR was created as part of a Jaeger Light Infantry Recon rework since the original unit was kind of a meme squad.
If you want to really get into arguing, the scope they use is only a ZF-4, a 4x scope originally designed for Infantry, not Snipers. It was only issued to Snipers because the Soviet sniper program encouraged the Wehrmacht to step up their own sniper program and the ZF-4 was already available in considerable numbers.
The G43 was and still is a semi-automatic rifle, a puny 4x scope doesn't change that.