Think about this, Bish.
A company commander on the front line would first call Batallion HQ for their Air liason to task ground support.
Batallion HQ would task air support to the company through the Air liasion BUT it is no good HQ talking direct to the actual aircraft as they cannot see what is happening.
The Company Commander, who is actually controlling that fight knows exactly where he needs the tasked aircraft so it is more use him talking directly to the aircraft instead of Batallion or Regiment.
This is still how it works today. In Afghanistan when support is needed it is Batallion or Regiment that tasks that support but it is the company or firebase commander on scene that actually controlls that asset when tasked.
I have actually done this quite a few times myself in Afghanistan and other places and the A-10 Warthogs that supported us have radios built in so the pilots can talk directly to the mudgrunts and hit targets that are called out.
THe allies in WWII had a slightly different system in that a air liason guy would be embedded into a unit and it was he who when called on would task and control air support from the flying cab ranks of Tiffys, Thunderbolts and Mosquitos.
The air liason guys would have callsigns of the aircraft flights/squadrons in their area and could call them in directly.
Now the tasking goes from front to Batallion/Regiment. The task is then sent to the nearest flight and the callsign sent to the scene commander who then directs the tasked aircraft or artillery and on occasions, both.
So, it is quite common to find the FUG 5&7 in Company commander vehicles or if not installed, an acompanying 251 for deployed infantry with the Panzers. The Germans were the first to employ combined operations. THe Allies learned from them and from the Blitzkreigs that employed the combined operations.