IMO this is one of those many situations where gameplay trumps semblance of realism. Another example of mechanics that are good for gameplay but would be nonsensical in real life is at grenades and panzerfausts causing engine damage when shooting at the front of a tank. Or cav rifles, guards, and most axis infantry literally just pulling guns out their ass some weirdly specific amount of seconds after you told them so just because you told them to (I’m talking about weapon upgrades lol).
Considering that they had no Halftrack and used the M3 one (Like in Special Weapons) I don't see a problem in using a bit of fantasy with the mortar HT.
I mean they now have the M1 81mm Mortar in the air supply operation drop, you could just say that it didn't need a genius to figure out how to make it a bit more mobile by mounting it on a Halftrack.
But I agree with the rest of what you say.
Guys, this whole concept of "what's one more inaccuracy if this exists already" is a dangerous rabbit hole. The game needs more authenticity, not less, and we should aim to keep what WWII polish it has left instead of making it into Battlefield V the RTS.
The riflegrenade smoke can easily be replaced by a standard smoke grenade with equal range. I'm also sure there are far more options than just adding a mortar HT. Pack Howi comes to mind, as they were sent in great numbers to the British airborne units.
Point is, we shouldn't dismiss the weight of historic authenticity. When there are historically accurate alternatives that can give practically identical in-game effects, we should always opt for those instead.