You don't even need a guild system.
It's a rather different genre, and the specific mechanics are different as a result, but this is conceptually a very similar problem as was suffered by WW2 Online back in the day. Originally, players could attack and capture nodes (townsin this case, rather than star systems) wherever they wanted, whenever they wanted. This caused loads of problems, including people taking towns that made no sense. The response to that was to create a high command for each side that could declare Attack Objectives, meaning players could only take objectives in towns with an active AO. This both ensured a concentration of players at each AO, and ensured that there was also some sort of direction (not necessarily
intelligent direction, mind...) and overall strategy involved. It had 'guilds' as well (in this case, squads), but the AO system was entirely separate. That said, I don't see the problem with allowing the formation of in-game player organisations; it's a good way to populate what's ultimately a very, very large environment with stuff. The issue is where you draw the line to prevent E

becoming EVE 2.0.
Now, there's obviously a difference between a hierarchical command structure - even a simple one as in WW2OL - in an objective focused game set in WW2, and an open world space sim billed as a game you can play how you want.
My suggestion would be that PP provides the perfect vehicle for a player-led, player directed mechanic
for those who want it (because if I want a player-directed group experience, currently I
can't play as I want, no?), but it would require significant overhaul for that to be appropriate. For a start, the rewards should be all monetary, so players that want to do their own thing rather than be 'told what to do' don't get penalised; the real benefit would be the gameplay, not special widgets. If that aspect must be retained, move it into a PP-independent relationship system exactly like we have now with the Empire/Federation/Alliance/Minors, with the special weapons becoming available after a certain relationship. You'd have to balance it so that it's only possible to have very good relations with one power at a time, though.
Second, strip out the grind from PP itself, and instead use many of the current mechanics to link PP and normal play. Have the powers give missions, available to players with high enough reputation, to ferry PP tokens and the like around for monetary reward.
Third, have expansion be directed by a player-led faction organisation that chooses objectives. This is the player-directed mechanic. Once a target has been decided on, each side should start getting sites in that system to either attack or defend vs NPCs, the frequency and difficulty of which depend on how many resources each side can move into the area. The more resources you have, the easier they should be. Likewise, players should be free to attack the other side's assets outside of those mission areas. The upshot of this is that players have to organise themselves to get the required supplies into the expansion area, to protect those incoming supplies - because the other side can attack them on the way in - and to attack the objectives in the target system... or indeed, to
stop the other side from attacking their objectives, if on the defence.
The objectives should be different for each power as well. For example, Hudson might have objectives that are straight up conquest, whereas Ashling Duval would have stuff like defending humanitarian ships. Tailor them to the power in question so as to provide some personality. They'd also only be able to be declared on systems that meet the prerequisites - Hudson isn't logically going to be able to attack an Imperial system without starting a war between the Federation and the Empire, so any 'police action' he takes should have to be directed against a Federation or independent star system. Setting up future expansion targets to be eligable is another thing that the player organisation would have to do.
Fourth, players who want to participate in PP, but don't want to be part of a player-directed organisation. That's fine; if the organisation is the Power's private mercenary army, individual players who want to do their own thing can be the Power's privateers. Issue them with a letter of marque and pay them for wreaking havoc in the opposition's star systems... or for delivering humanitarian aid to systems in civil unrest or whatever. Again, tailor the activities that get the player compensated to the power.
Finally, this all needs to be tied together, rather than operate mostly independently of the rest of the game like PP seems to now. The resources available to fuel expansion should depend on the overall state of a Power's economy, meaning that PP is tied into the 'normal' game at that point. The more PP-related trade missions that get done, even just the number of normal goods shipped about by non-aligned players, should all play a part. This, of course, incentivises PP players to protect their territory, and the other side(s) to try and destabilise it. It also means that the 'organised' PP players and the independents have some sort of relationship to each other.
It would also require at least a minimally effective in-game organisational tool, even if it's just a faction-wide chat, but preferably including some sort of in-game bulletin board system so that the current strategy can be explained, and to list future targets so people can work on getting those systems into a state where they can be expanded to.
The big overall advantages of this are that, first, it prevents a situation where all the incentives are perverse incentives that will ultimately lead to collapse (that is, the situation as it stands now), and second, that it creates a community around each Power. As anybody who's ever played a game like Cybernations knows, even if your mechanics are as deep as a puddle in the middle of a 30 degree heatwave, if you have a strong community, that doesn't matter. As it stands, PP doesn't have the engaging mechanics to stand on its own, and it totally lacks any effective way to assemble a community around each power. It really needs one or the other, ideally both.