Presently, there's a few other functions you unlock as you complete the quests for the place and build it up:
- send teams (either Security or Logistics) to take settlements for you without you having to go there yourself, and start a City Plan there
- force Leveled City Plans to upgrade right now
- 'research' increased range for Caravan, Communications, and Power Transfer plots, and the ability for Caravans to link different 'worldspaces' together
- use the Science Department's "labs" to do crafting without your player-character requiring the perks and using the Virtual Resources to pay for it
- make it so for any specific plot design, if one instance of it has hit level 3, all other instances of it can skip the time requirement on leveling up too
Those things combined mean that once your HQ is fully armed and operational, you can basically instantly add fully leveled up settlements to your network.
It's been pretty strongly hinted that there's still more things to add too. kg has repeatedly mentioned that Science Department still doesn't have
something it was meant to, and I would guarantee there'll be more functions added by "Chapter 3" and what it's going to be doing.
Some of the rooms are used as pre-requisites for things too: the Gym at least is required to be built before you can do the "Cross-training" for Security Department to make them use AGI+STR for their Energy value instead of just AGI.
However, it's worth keeping in mind that it's all been designed with the notion of Addon Packs having a
lot of variables they can play with for what
they want to do with the place. I
think this is why if you poke around in the place you'll find a few things that appear to not do anything right now - Admin Department ends up with a Therapist's Office for example, or there's a few rooms that mention "Pre-war Research".