Without being an expert on the cyberpunk lore much (the intricate details of the CP2020 and so on), from my understanding I'm more inclined to go with
@Suhiira 's reasoning and deductions.
I don't think Arasaka (or Militech, etc) need to have something akin to MAX-TAC at their Night City HQ at all times in some sort of readiness. An army of capable "corporate goons" likely does the trick with more flexibility in terms of replacements and deployments than having a highly specialized ("elite") combat unit as super top of the line tool. They surely will have their heavy hit teams depending on how you want to categorize or specify those but I'm guessing they don't necessarily need something like a corporate MAX-TAC (on the same level) .... when they can call in NCPD's MAX-TAC (cheaper, same crap) or when they can likely deal with the threat themselves due to their general security measures.
The corporate city center is already highly policed or secured compared to other areas of the city, meaning the security and structures themselves help in deterring cyberpsychos or threats. I doubt Cyberpsychos plaguing the immediate corporate center are a big issue due to said security.
And speaking about Cyberpsychos, why keep some corporate MAX-TAC on standby at all times when you have this guy (Adam Smasher, Arasaka):
Assuming you even get remotely far into their headquarters - this is likely where some nutjob meets his end once they run into him.
Either way, I realize this thread has a heavy corporate reference or focus, but in the end I think nothing beats the concentrated power of national military forces. I read many articles saying that despite the heavier fractured world and power shifts towards international actors like corporations who retain their own "armies" in essence, many 'superpowers', even those with better old glory days, can put any of them in their place if they have to because they got the bigger stick.
Whatever big stick the corpos might have, the fractured US (or similar powers) can likely whip out an even bigger stick.
As I read and understand it, the Free State of North California as a 'sovereign state' not part of the Union anymore retains its own classic miltiary forces. While they can probably not withstand the Union forces I'm inclined to believe their heavy hardware and troops would also already be able to roll over corpos stepping out of place in the state.
Chances are we will not see any NorCal military forces in any notable capacity in the game however. But time will tell.