I also think this should not be implemented the way you suggested it in your first post. In my experience a.) the faster you move the less you will actually hit, if anything at all(you mentioned that but still just have to point it out again) and apart from that you might even trip over something on the floor that you did not pay attention to because you were moving looking down your sights.
b.) WW2 weapons were much heavier and way less userfriendly/ergonomic etc etc. than modern assault rifles.
c.) Drills have changed a lot and have not! Check out some manuals on squad tactics from back then or even up to now. You got the cover group and movement group exchanging their roles all the time in order to advance towards an enemy. (COVERING FIRE .....)
On the other hand, reflexive shooting and even shooting stances have only lately changed due to new and as said above more userfriendly hardware. Meaning even if you compare rifles from the 50-60-70ties their recoil would hardy enable you to shoot properly while moving if at all, unless you want to hurt yourself or waste ammo. Below i got a little comparison of two "modern" assault rifle and two main German WW2 rifles/mps.
d.) Finally, even sights have changed. Getting your K98 sights properly aligned is much more time consuming and difficult than looking through your average commando holo sight or even light reflective dot sight. Nothing which was available between 39-45. :IS2: So moving quick and shooting/aiming properly.. NO
G36:
G36: 3.63
kg (8
lb)
G36V: 3.33 kg (7.3 lb)
G36K: 3.30 kg (7.3 lb)
G36KV: 3.0 kg (6.6 lb)
G36C: 2.82 kg (6.2 lb)
M4:
Weight 5.9 lb (2.7 kg) empty
6.9 lb (3.1 kg) with 30 rounds Length 33 in (838 mm) (stock extended)
29.75 in (756 mm) (stock retracted)
Mp40:
Weight 4 kg (8.82 lb) Length 833 mm (32.8 in) stock extended / 630 mm (24.8 in) stock folded
K98:
Weight 3.7 kg (8.2 lb) - 4.1 kg (9.0 lb) Length 1,110 mm (43.70 in)