The beauty of CONCORD is that it operates through the implicit use of force, not through overt demonstrations of military might and prowess. To use a practical comparison, they're like a U.S. carrier battle group showing up in a troubled part of the world: when they arrive, or even when there's a threat of their arrival, heads turn. And as someone on active military service I really do have to admire their efficiency when it comes to this.
CONCORD clearly has the muscle and resources to dislodge the Nation if they wanted to. If you don't believe me just look at the Code Area Inquiry and the ISHAEKA reports, which speak volumes as to highly-specialized capabilities and what they're capable of when someone lights a fire under them. Another example is the Elder attack. They crammed how many ships into that station to provide the power to reboot the computers?? There's no way an Empire military could rally up that many ships on such short notice.
And then when they told the Empires "oh no you don't: this fighting ends now" (not in those precise words but I'm sure you get my drift) as soon as the computers were back on in Yulai, the Empires listened. The fighting stopped, abruptly, because for lack of a better phrase God had spoken. Only CONCORD had the power to stop the fighting by flipping off the stargates, and in the end that's precisely what brought the Empires to heel. It was an "uh-oh" moment for them: be crippled and vulnerable to CONCORD fleets, or obey and see what comes next?
After all that why disrupt intergalactic commerce with sanctions and retaliations, Lallara, when you can let the Empires have their safety valves (the militia wars)? CONCORD gets back to being the "bad boy on the block," and the Empires go back to their fighting. CONCORD remains in charge precisely by being the implicit force that prevents things from getting out-of-line and escalating any more than this, while the Empires weaken themselves with more fighting.
All-in-all everyone wins. Commerce continues (CONCORD of course takes a cut through taxes), the politicians can be elected on militaristic platforms, the people are safe and secure (for the most part) and can go about their daily lives, the militaries are confined to their systems, and the capsuleers get to go fight each other in an authorized fashion.
And after going through all this, why commit resources to fighting Nation when they could get someone else to do the fighting for them? Oh sure, a CONCORD task force on the battlefield would be a Grade-A morale booster, but realistically we were handling things (almost) fine on our own. Note the use of "almost": there were definitely some failures in the pre-war runup (but honestly I think that was more due to CCP scripting of events than anything else).
CONCORD had to have known that, walking into this war with Nation, all they had to do was dangle ISK in front of capsuleers, and voila: you have a proxy Navy to do your fighting for you. They also (for a time) nudged capsuleers in the direction of continuing the fight by furnishing points-of-contact and -coordination to us. Haeldone Dorgiers was a perfect case-in-point: a CONCORD officer who almost overnight became our default go-to guy inside the most pervasive organization in high sec.
Sure he showed up on the battlefield from time-to-time (I remember being in a fleet that ended up saving his butt out in Monalaz), but for the most part his role in all this was to provide us crucial information. It was tacit approval of what we were doing by CONCORD, without themselves committing a fleet or army. And that's what makes CONCORD's tactics so beautiful and admirable. We do the fighting, they point and say "go here," and all along we know they have our six.
But in a way though that's also their Achilles heel, and I think that Kuvakei knows this. He shifted from fighting CONCORD to fighting capsuleers because we're a disorganized rabble, all things considered. There's no sense of unity and no "common platform" that we all agree upon, short of opening fire on Nation ships whenever and wherever. CONCORD is probably complacent because in all their history they've never confronted a seriously-overwhelming threat. I think that the Elder Fleet attack may have actually increased their complacency: it showed they were still the ones in charge after all the dust settled.
It would take a real bone-crunching event to bring them to their knees and "rattle their cages," and I mean a really bad situation. Taking out the CONCORD HQ in Yulai wouldn't do it: all they'd have to do is relocate elsewhere and start with what was already on-the-ground. But if Nation could eliminate those security safeguards for a sustained period of time, that would do it. Especially if CONCORD couldn't get them all re-established and had to code everything at, say, 0.5 status.
