You aren't getting it.
Command is an inappropriate term. How does infantry, or even armour have a role in "commanding" the counter battery task. The infantry has a part sensor role but its forward artillery observers who are also sensors and more importantly are the link into the effectors net. Why burden the infantry with that. They are already busy in their own fight.
Armour are not infantry fighting in vehicles. One can go so far as to say that armour fights mounted and infantry fights dismounted (and accompanying armour in IFVs isn't really so much fighting mounted as being forced to fight mounted on occasion when things go wrong). Neither "commands" artillery - its a cooperative process where the supported arm is the dominant partner.
That can happen but isn't the model of employment. Again, why burden the "lonely infanteer" when there is a team of experts supporting her in her fight?
Yeah. That does happen. I must admit we're short of the gold standard in that. While the FSCC at all levels is the hub around which all that ought to happen, it still lacks the necessary automated linkage that should merge all battlefield sensors into a system that automates the appropriate effector response. We're still pretty much operating an analog system in a digital world. Luckily the recognition of that deficiency is there and a project exists (
Joint Fires Modernization). Unfortunately I do not know its progress (it ought to be in implementation by now but I don't think it is - FOC was predicted for 29/30). I'll spare everyone my whinging about how the army has shoved the priority on this time and time again but at least now its pretty high to the top.