The Yulai Siege
In YC 106, a group of capsuleers united under the Zombie Inc corporation laid a successful siege on one of the Yulai gates. It is important to know that in this period, Yulai was the major trade hub of the cluster, the Jita of its days. It is also considered a high security system, carrying a security rating of 1.0.
But the arrival of the Zombie fleet caused major disruption of the trade, as their smartbombing battleships destroyed anyone entering the system indiscriminately. The combined firepower of the sentry guns & Concord ships was unable to take these ships down, as the Zombie Members had brought in shield logistic ships, allowing them to maintain the shields of these sieging battleships despite the heavy concentrated fire from law enforcement. An ancient holofeed can be found here: Zombies Smartbombing Yulai
In the end, as thousands of ships already had perished, among them countless Concord ships and hundreds of capsuleer ships; Concord Command Personnel saw no other way out than to enforce their far reaching powers. They ordered the Zombie fleet to cease their aggression and stand down, else they would shut down their capsules.
The Zombie fleet declined to comply, believing that Concord would not dare to enact such desperate measure as it would cause a major backlash in the capsuleer community. But they were proven wrong when CCP Lickspittle followed through on his threat and temporarily shut down their capsules, for the duration of their sentence.
The aftermath of the Siege
The backlash was, as expected massive, but the capsuleer community proved to be sharply divided, between those who believed capsuleers should be above all laws and those who believed that capsuleers should not be allowed rampant freedom within Empire space.
During this, Concord decreed they would upgrade their response teams and also improve their weapon loadout, to prevent any capsuleer deactivation in the future resulting from Concord's inability to resolve an illegal combat situation directly.
In an effort to create a permanent solution, the CONCORD Inner Circle organized an emergency meeting.
During this meeting, the Jovian delegation offered to build a new line of Concord Battleships, fitted with appropriate Jovian technology to deal with any illegal capsuleer threat. These ships would become the Concord Command ships, using extremely advanced technology to eliminate any ship in record-time.
Only Concord pilots who were screened by the Jovians would be allowed to pilot these. It was also made very clear by the Jovian delegation that any attempt, no matter how small, to analyze this Jovian technology would bring down Jovian wrath upon them.
Considering the technology the Jovians shared with those who complied, it was enough to ensure that no nation would try to steal this technology for their own, lest they be left out of any future technology shared by the Jovians.
A change of combat doctrine was also adopted. No longer would Concord solely focus on the first offender, but they would now spread their attacks on multiple targets, disrupting any future logistic fleets brought into action against Concord.
However, the standard ships were still sent in first, to disrupt & destroy the offenders. Only when the initial wave of standard Concord ships failed to take down the aggressor, the Concord Command ship would jump in to deal with it by instantly destroying the hostile ship.
Speculation on the instant kill tech provided by the Jovians
The technology used to instantly destroy a ship is unknown, but a variety of theories exist. Most of these revolve around the assumption that the Kill beam isn't actually an energy beam, but an extremely advanced electronic attack weapon focusing on overloading subsystems, presumably the reactors or the shield generators. Overloading a ship's reactors would surely cause its immediate destruction, no matter the size of the ship.
There is even a precedent to this theory, as Empress Jamyl used an ancient weapon to wipe out an entire minmatar fleet with a single shot during the Battle of Mekhios. It can be assumed that the Jovians got a hold on a similar technology that works on a smaller scale, wiping out ships with a single shot.
Whatever the theories & the workings considering this kill beam, the results are frightening. No ship in all of the Eden cluster can stand up against this powerful & deadly weapon! There exists no known defense against this. Hence, if you commit an illegal aggression in high security space, you are unable to escape the destruction of your ship if you are a capsuleer.
The results of the Concord Command ship deployment
Ever since, the power of the Concord ships has remained unchallenged by capsuleers in direct confrontations. Ever since, most capsuleers attempted to defy Concord by outrunning their interception fleets.
From jumping around in system, to using Wormholes & Cyno's, it's all been tried & Concord adapted. But no successful direct confrontation has ever been reported since, but not by a lack of trying.
You can read about the latest large attempt to bring down a Concord ship here: Capsuleers fail to organize a gank on Concord where anarchist capsuleers gathered hundreds to take down a Concord Command ship, only to fail spectacularly.
There have been reports of Concord ships being destroyed since, but those were in most cases regular Concord ships, not a Command variant that comes with Jovian tech aboard. Only in one cases a possible Concord Command ship has been destroyed.
During the Battle of Caldari Prime, the Shiigeru shot down a Concord ship, refusing to stand down by order of Concord, resulting in the fabled fight over Caldari Prime. Do note that in this particular case, a 'Marshall' class Command ship was destroyed. It is unknown if they carry the same loadout as the Concord Command ships piloted by the Concord Police commanders.
Do note that most capsuleer ships that break Concord law get destroyed by the regular Concord Police ships. Only when you are able to outlive the initial wave of Concord ships, the Command ship initiates the attack, spelling certain doom for your ship.
For a more behind-the-scene look, you can consult this article: Eve History: Zombies defied Concord, leading to their revamp