In lore its an alliance of independent states united by a parliamentary democracy, civil service, property law (with the exception of anarchy factions), some social protections and a shared economic infrastrusture.
Your description is not really reflective of the noted difference between the alliance's government and the federation or empire. What you described is any government. What differentiates the alliance from the fed and empire is that these member states are still independent and have only joined the alliance so that they aren't annexed and bullied by the federation and empire. That's it. That's their point for existing otherwise these member states would remain independent and unaffiliated with anyone else because that's how they would rather be. The alliance is a necessary negative for them and exists to function only so far as needed.
In practice it is a player organisation with many shared values chief of which is liberty, freedom. As such the bear is only aggressive when poked or woken from a sleep.
The feds and empire should be big players but the player Alliance's support for the independents in the Pleiades seeking autonomy and our assistance in those goals enable gave us the skills and respect to work the Witchhead nebula multi faction BGS. Our members hard work in the game expanding the count of its citizens in the bubble and out while diplomatically seeking allies and friends has earned us the rewards due. The empire and the federation already had larger starting faction/system counts by far and naturally that is where there players attentions have focused.
I'm not really interested in the player group (pp) take on the game's lore and factions since they're not being reflected by the narrative. If they were, then that would be another story.
A divided power will never be as strong as a united one. The alliance has only one PP faction and various diplomatic bodies and executable bodies which work together socially and strategically. The empire is getting its act together in this regard also - however the federation remains fractious internally and externally. Currently the Empire and the Alliance and certain independent powers have strengthened their strategic partnership in response to Federal aggression and betrayal.
In the lore, the quantity of PP powers has no impact on the function of the given super power unless those different powers differ in the given topic being looked at and this leads to narrative explaining as such. The powers within a super power are not mutually exclusive in most areas, that's how they rose to become powers ...they align with the people of those powers greatly ...what makes them different powers is that they differ in a few areas or have ties to certain powerful people.
Powers are not competing governments, they're just focal points of personalities that garner significant following.
The fact that the alliance has only one can be seen as a sign of weak cohesiveness or weak exceptionalism within the alliance. No other powers would need to exist because no other single entity can get enough following or nobody else is looking to become a leader of people because they're satisfied with where they're at now and dont want anything to change. The people within the member states are not interested in the government or other people, just themselves.
Where as many powers would indicate the public is very active in government and others. Driven both to follow and lead change.
The central reason for the player Alliance major faction existing is for everyone to have fun and try not be antisocial while doing it, we maintain a balanced view on the thargoid war with our players whom the majority represent the defensive approach, some the anti-ax approach and a minority the aggressive approach. We disagree all the time but we talk about it and have a laugh doing so. But we never come to blows thats just not the RP. We have strategic partnerships in place with AXI and organisations seeking de-escalation. Our members work hard to maintain the security of the exo-colonies as a place where commanders can enjoy conflict, companionship and profit without political concerns.
again, not really caring about the player created mythology existing outside of the narrative and lore. The main reason there's one alliance pp faction and thus one player alliance major faction has nothing about wanting to have fun or not being anti-social or what the players want at all. It's because that's what fdev created 7 years ago for powerplay and they've left it as such so you have no real choice but to work with what has been given. Nobody participates in powerplay to be anti-social.
im not even going to comment on your last paragraph it just make my head hurtee very muchly
Sirius replacing the alliance thru a defense pact that involves concerns that the alliance charter wasn't created to cover makes perfect sense. And for them to create this, this way has precedent in reality. It would be trivial for Sirius to start their superpower off this way, and then make an argument once they get a critical mass of membership to this pact that they could create a better government in general than the current alliance charter and expand that pact to include a full charter/consitution and the alliance would be dissolved by it's member states agreeing to dissolve it en-masse.
The alliance is a weak central government that exists only because something bigger than any single faction was needed to oppose the fed and empire military and economic arms. It would be defenseless to oppose it's own largest (or one of) member state from effectively replacing it because it's own power comes from that member state as would the alliance's own power to do it's job for the other smaller member states. Where the power of the alliance goes, the vast majority smaller states will have to follow.
(edit, and sure, sirius isn't part of the alliance right now. But it wouldn't need to be to effectively replace it. It would just need to court the larger members of the alliance super power and by being independent itself, it would be easy for them to take over. this would make far more sense for Sirius than starting their own 4th super power with the remnant independent systems not already part of the alliance)