First of all, let me start by thanking you for a wonderful game!
Secondly, I applaud your decision to develop such a feature as Planetary Supremacy: it's truly is a great way to increase replayability as well as give substitute for each faction's campaign!
That being said, let me now focus on the points that - in my opinion - could make the experience much better

NB: I finished 2 PS runs:
- As Tyranid vs Marines & Sisters (2nd difficulty)
- As Necron vs Tyranids & Sisters (3rd difficulty)
1. Major Gripe: Lack of fighting the actual opposing factions
In both of my runs so far I had only ONE case where I fought each opposing faction more than once - when playing Necrons and fighting Sisters after finishing off Tyranids. In all other cases we ignored each other until the moment I assaulted their HQ.
This feels really awkward as we have to decide the main 2 enemies, but end up fighting random minor factions 90% of the time during the PS. It also creates an issue of steamrolling hexes towards enemy's HQ.
2. Medium Gripe: Boring generic maps
While the hand-crafted HQ maps provide for an interesting combat, I've noticed that the random maps are kinda boring (except for the ruined city with trenches, it was the only type of map providing fun). I'm mostly referring to deserts and plains covered with random rocks - these maps lacked any interesting landscape to create challenge or force me to think about positioning of my forces.
3. Medium Gripe: Only one army
Having only one army made me feel that my hands are tied in terms of variety: I didn't feel that I could play diverse builds for which I actually had upgrades. I also think that the one global army is the reason for the steamroll effect that causes no1 gripe I have.
4. Minor Gripe: Dispersed armies of minor factions
A bit connected to the previous gripe: I noticed that minor factions have their armies fragmented and scattered around the place. I'm quite sure that it's intended, but it implies that Player has two approaches as well: to fragment their army as well to hunt for enemies in order to clear the map faster (risky), or to hold the forces together and sweep the map for longer (no risk at all). Now, I myself was always choosing the first one, but only due tot he fact that I didn't want to waste my time - although it really bugged me that I was forced to use less effective & more risky option cause the other one felt as a chore.
5. Minor Gripe: Sisters always starting on the same side of their HQ?
Can't be sure if it's always the case, but in my current experience Sisters started both times in the same corner of their HQ, which - if true for all times - will make replaybility for HQ battles much worse due to predictability.
6. Minor Gripe: Opponent Army Compositions
I understand that I didn't play that much, but I saw a couple of weird armies that the AI has come up with that seemed to be rathe ineffective:
- In my first run, the Space Marine AI had 2 Lieutenants & 3 (!) Priests in his army. The rest of the forces were more or less okay, but the 3 priests really were the reason I dispatched him so easily.
- In the second run, the Sisters I fought two times insisted of having 6 (or even more) units of arco-flagellants. Maybe in human's hands they could be played differently and provide the threat, but in the case of the AI i was just a guaranteed easy win for me as they didn't pose any threat whatsoever.
-----Suggestions-----
I do consider that such many of the tings I experienced were actually what was intended by design, but as a great fan of such games I do believe that things can be done differently to provide an even better experience

With that out of the way, here's my five cents:
Have Army tokens (and Armies cap as an additional attribute that can be affected by 1 of 4 special resource nodes, with say 2 armies being a default value, but starting with one) that are actual entities on the PS map with the move action:
a) Army can move up to two friendly hexes, but uses all remaining move points to initiate an attack into enemy hex (defeated army token retreats to the nearest friendly hex after the battle, provided it had units remaining)
b) If army doesn't move, it's considered to be in R&R - to heal up injured units (yes, units injuries should really be persistent between combats to avoid steamrolling)
Army would also have a limit on the HQ units, that would help shape it's respective build.
I do believe that such feature would make steamrolling much harder, and would ensure that we have much more combat instances with actual opponent factions we choose at the start of the run. Yes, it would prolong the run, but it would also create this bigger "campaign" feel that people in the steam forums (me included) really want.
This would also give more meaning to the way the unit recruitment works now: since we don't have reserves, I always found myself to be in surplus of requisition points.
------End of Suggestion-------
Looking forward to new factions and PS feature improvements!
Keep up the good work
