Heavy Mortars are a strange beast, just like the Light Mortars.
They are NOT a bad weapon, in fact they are quite amazing on the right setup, they even make ships that would otherwise have to downgrade their medium ballistic mounts and use small ballistic (like the Enforcer) retain a very respectable damage potential instead.
But it does not end there. The heavy mortar does especially well when you install it on an Overridden ship with a lot of medium ballistic slots and you don't want to also spam vents to sustain the absurd flux generation of things like Assault Chainguns (wich are getting a nerf next patch by the way, should make Heavy Mortars even more worth it).
As an example of a ship that can make Heavy Mortar spam very much worth it, I am currently using heavy mortars on an overridden, 20 FP mod ship (from Hazard Mining Incorporated) called Roach King wich has an incredible amount of ballistic slots facing the front (7 medium slots of wich 1 is energy and 2 are hardpoints, 1 large ballistic on a turret and a plethora of small ballistics, there also are a lot of missile slots but I'm not actually using those) but barely any flux dissipation to install expensive stuff.
The one problem of heavy mortars isn't really their inaccuracy or comparably worse projectile speed/weapon range, it's the fact that not many ships have enough spare medium ballistic slots to properly deploy it. The real problem therefore is the fact that it's way too cheap for a medium slot. I could see it being much more widely used if it cost a bit more (thinking about 8-9 OP) with improved fire rate while retaining its amazing flux to damage ratio.
P.S: I've also got mods that introduce (rather expensive) hull-mods that significantly buff projectile speed and accuracy when combined, potentially making Heavy Mortars (and Arbalest Aurocannons by extention) quite potent at range. You might consider cheking them out for your future campaign
1) More Hullmods by PureTilt:
https://fractalsoftworks.com/forum/index.php?topic=18474.0 (Includes Particle Accellerator that increases projectile speed by 35%)
2) Ships/Weapon pack by Dark.Revenant :
https://fractalsoftworks.com/forum/index.php?topic=11018.0 (Includes Gunnery control AI that improves weapon tracking and also increases projectile speed by 35%)