Right, but a counter fire battery fires mortars or similar exploding ordnance towards the location where the inbound weapon was fired. The anti-mortar is firing smaller, non-exploding rounds.
There has to be a big difference between say, a dozen 20mm bullets (albeit a depleted uranium bullets) falling back to earth near the perimeter of the base, and a dozen 60mm mortar shells each with 3-4 lbs of high explosives landing in a neighborhood.
Of course, I believe if we had a policy of always firing the counter fire batteries, people would be more likely to chase off the insurgents from their neighborhood.
Ya THINK?!?!
Unless they hit your house.
Something I didn't think of until I read your post is that counter battery and mortar defense do two separate things. Counter battery kills the guy trying to kill you, mortar defense saves your troops.
We can get around the need for counter battery by using other assets.
A smart round from a 81mm or 120mm mortar might work - you'd only need to send one if it is terminally guided. The only one of those that is operational so far, that I know of anyway, is the Swedish Strix from Bofors, 120mm. (The Brits - BAe - tested an 81mm smart round but the army there killed the project a while ago. US smart 120s are in development but no contract has been awarded yet).