Now you're talking my language: What's the story?
Well, there's airburst, targeting a hex bypasses most defensive mods. Not too much damage, but it does hit everything in the hex. Also clears infantry pretty well.
Anti-personnel mortars are useful for clearing infantry from long distance, not too many options for that.
Flare mortars aren't the most useful things unless playing with night rules. (Under TW/TO rules, Flare LRMs don't actually exists as usable munitions.)
There's smoke option, never a bad thing.
Spheroid mortars also have semi-guided option.
Okay, not that special but you got options. Never know when they might come handy.
But, I recommend to not use that, unless you face APDS. Shooting LRM against AMS actually makes the better damage output than the mortars with same class, because mortars are too weak. There is a reason why it is hard to see - that's just because it is simply outdated.
Mortars aren't a LRM replacement, or even an alternative really. Rather, they're long range crit-seekers. They're not that stellar against 'Mechs unless those have weakened armor or even holes in it already, just like SRMs. Against vehicles mortars are far more deadly due to their many individual hits.
Now, one might suggests using LB-Xs and the like, but those don't offer indirect fire option. Enemy armor column rolling somewhere? Get a spotter in position and fire a bunch of mortars and watch the enemy vehicles getting immobilized or whatever else nasty things crits tend to do to vehicles.
It is unfortunate mortars are pretty rare. Off-hand, i can think of only Gurzil (or some such), an experimental version of the Ha Otoko, and the Ant Lion. The last is excellent if very specialized mortar carrier, but pretty exclusive and arguably too specialized for general use.
Wish there were mortar configs for some Omnis. Not always useful, but having them as an option would be nice.