Well, hold on a second.
The Licori are in the same general direction from us as the Romulans, and they're no closer to our borders. Its not like the Sydraxians or Lecarre, who can harass our flanks. In a war situation, I'm really not seeing the strategic value of the Arcadian Empire's location.
There's more to having an ally than where they are on the map.
The Sydraxians are/were a threat not just because of their location, but because just by
being warlike and politically separate from Cardassia, they become a separate force Cardassia could use to harass us. One we hesitated to remove because they benefit from Cardassian protection and because of our natural war-aversion.
The Lecarre are/were a threat not just because of their location, but because they have unique capabilities no other known species can match
Focusing on
where the Licori are isn't nearly as important as the question of
what they are, and whether they would be a problem for us in the hands of someone determined to cause us trouble. Which I'm pretty sure they would be.
Like we're trying to engulf the Romulan Empire.
I wouldn't actually mind a situation where we have a negotiated arrangement with the Romulans to preserve the neutrality of those nations in order to
avoid engulfing Romulus, and instead providing a layer of neutral "buffer states" on Romulus's coreward flank.
The problem is this situation where the Romulans are trying to slip in and gain major advantages that can be used as leverage against us, by indirectly profiting from
our sacrifices and efforts, without consulting us. They have a right to have their interests taken just as seriously as ours, but that doesn't mean they have a right to passive-aggressively take whatever they want without even talking to us.
"Adversary", "I wouldn't mind the Licori having a government that ..."
Seeing another government as an 'adversary' is the job of our government, not of Starfleet.
Seeing another government as 'our special friend, ignore what they do, it couldn't possibly be a problem or a threat to us' is ALSO a job of our government, not of Starfleet.
One of Starfleet's missions is to defend the Federation. Starfleet cannot
possibly defend the Federation if it does not at least seriously consider questions like "is this action, taken by a nation that has historically struck at us when it thought it could, and which has
never been fully friendly or open with us, a potential source of harm to the Federation?"
Maybe someone else should make the decision "is this a problem? What should we do about it?" But there is no coherent way in which it makes sense for Starfleet to
refuse to have an opinion. Where we just don't care about what our neighbors do. Where it's "not our job" to think about and prepare against the possibility of them taking hostile action. On the contrary, that is
exactly Starfleet's job.
"I wouldn't mind" - this right to self-determination (see also Prime Directive) includes the right to do things you don't like. You are advocating the position of 'if we don't like the government they have, let's change it'. Perfectly fine for an Empire / colonialization quest.
No,
you are refusing to recognize the difference between "push back" in the sense of "resist Romulan actions,
specifically the Romulan actions, that are intended to install a new government where no government now exists" and "try to topple an existing government so we can create one."
This is a massive black/white fallacy. You imply that if I do not favor
zero action, I must favor
infinite action, when infinite action would be 'imperialism.'
This is exactly why I dislike the wording of the vote, as
@Briefvoice does. By including "we are not colonizers" in a vote choice,
@OneirosTheWriter has implied that ONLY colonialism is a reason for 'pushing back.' The only reason we might oppose having a large foreign government that has sought to strike at the Federation multiple times in canon gaining a puppet state right along our border.
I mean gee, don't other reasons occur to you? They certainly occur to me.
Now see, we did in fact topple the old government,
entirely by accident. The question is not whether or not a government gets replaced. It is
who gets to replace it.
In my eye, the only really good options are "the Licori alone," or "a joint Licori/Romulan/Federation negotiated agreement." Having the Federation dominate the replacement process isn't good but at least it doesn't harm the Federation. But having the Romulans dominate the process is just terrible from the point of view of both us
and the Licori, especially any Licori who didn't want to be a Romulan puppet state.
If they want to talk to the Romulans and accept Romulan' help, what, except for "our political goal as defined by Starfleet is to not allow the Romulan sphere of influence to grow", gives us the right to interfere by "pushing back"?
Does that mean that if
some Licori want to talk to Romulans and accept Romulan help, and if the Romulans are active and vigilant to provide this help quickly, then
all Licori should be expected to bow down to the group of Licori that had the bright idea of seeking Romulan help? How is that fair to
anyone? How is that protecting anyone's self-determination, except the "self-determination" of a handful of Bene nobles?
I mean, this is going even farther than the TNG-era Prime Directive. You're saying that if
one part of a species brings in a second party from outside help, that this constitutes 'the affairs of their species' and should not be interfered with. Even if the rest of their species has no interest in this intervention by the second party.
This is related to the flaw I'm now trying to lampoon among the Licori, the one that leads (when taken to extremes) to tolerance of the loathesome practices of
Korannon Kortennon, and to a society where the central government fails to restrain its provinces from developing star-breaking devices and testing them in ways that may threaten the Federation. Because that would constitute
interfering in what someone with power wants to do.
Mistaking the actions of just any person who has power to affect the situation, with the kind of important and sacred thing we use words like "sovereignty" and "natural development" to describe, is unwise.
We engulf and eventually assimilate both the Romulan and Klingon Empires into the Federation making one massive federation? 
