My guess is that you can do corrections for mortar and howitzer fire and not grenade launcher fire because a mortar and a howitzer is that a grenade launcher is a hand held weapon, a mortar and a howitzer is not.
You're on the right track — but the difference is actually a bit more basic even than that (note e.g. that the Mk.19 grenade
launcher isn't exactly handheld either):
The significant differentiator here is that howitzers and mortars are indirect fire
weapons, whereas grenade
launchers are direct fire
In indirect fire, grenades are fired on a very high parabolic trajectory — most often over terrain that blocks the target from the weapon's location — and land on the target tens of seconds, up to a couple of minutes, after being launched. Sights don't have a "crosshairs" you place on the target; instead, you fix the sights on a reference and then start dialling the azimuth and elevation. Hence a need for spotters, and corrections.
Direct fire is line-of-sight. Even 40mm grenades and rifle grenades (which for some reason seem to be omitted from the game), which have a relatively high trajectory due to being slow, still are primarily direct fire. Projectile flight times are, compared to indirect fire, relatively short (a few seconds, tops); sights work basically the same as on any firearm. The gunner can always observe where rounds land and adjust his point of aim accordingly. Hence, spotters don't really enter into the picture — the gunner is his own spotter, as it were.
use these weapons in an indirect fire mode to lob grenades over terrain obstacles, but they don't really have sights for that use — you'll basically fire at random. Sort of like firing a rifle around a corner.
51mm light mortars ... often don't really have any sights either, beyond a painted line along the spine that helps give you a general hunch that you're pointing it sort of in a desired-ish direction. No real help to gauge elevation.
I'd say their main use is to fire ordnance like illumination and smoke shells, where precise aim isn't really a big thing. When used to fire HE, again, you're back to firing mostly at random. It's highly unlikely you could even effectively target a specific 10m hex.