By definition the Panzer II Luchs is a reconnaissance tank, and yet in the game it functions as a light tank. It's almost as if real life combat roles and weapon/vehicle charactaristics are sometimes bent into different roles in the game to serve gameplay.
An extra shell per barrage is not weak.
As for vet 5 the +20% damage increase is pretty huge.
Half the reduced scatter perhaps, but its base scatter values are much better.
Better scatter for all fire modes is also much more valuable mid-late game (when you largely rely on autofire) than just a barrage scatter reduction other mortars get.
You're forgetting that the ISG has better scatter values, which largely offset its slightly lower AOE profile.
In both autofire and barrage it also has higher ROF because it doesn't have as much wind up and wind down time as other mortars.
ISG has 8.925s reload vs 10.625s reload of GrW 34 for autofire;
and 5.075s vs 5.5s for barrage.
Vet 5 according to your post is +15% not 20% and that is great but the Leig hit the field later than mortars and by the time it reaches vet 5 i dough it impact would be sufficient.
My points stand the unit comes later the mortar is more expensive and it is less cost efficient both in base performance and when equally vetted. (since it can not retreat or used behind shot blocker effectively)
Compared to the M1 Pack OKW it greatly inferior. As a faction the OKW going T1 has more need than USF has, for what you describe as "a howitzer role ingame" since USF has more stock and doctrinal options. Note that USF has little reason to have superior direct fire weapon than Ostheer this early in the game after their changes in tech.
Even with changes in vet the unit will remain mediocre although it one of the few indirect fire options for OKW.
Again one can simply swap it with the mortar that better fits the faction while fixing many issues in the process.