Last Guy in the Airlock
Give my wordiness, I thought I'd nutshell the topics for everyone-
Is Paramount+ a good shepherd of the Star Trek brand,
The first season of DIS was, for me, disappointing. Extended riffs on two classic stories, but both went on longer than they needed to. Season two was amazing, though, and leads to the upset in the captain rankings I suggest below. Since then, the series fulfills the promise of strange new worlds, etc.
LOW, as you note, gets Trek: it is able to mock it without undermining the setting or cheapen other instantiations. That's an amazingly fine line, and it seems to be walking it well.
At the same time, PIC left me cold and nostalgic for better Picard stories, and I couldn't get through an episode of Prodigy because all the tropes it was drawing on were Star Wars and not ST.
and why do people continue to hold James T. (the T. stands for "Terrific at Chewing the Scenery") Kirk in such high esteem?
Boomer and Gen-X nostalgia, and the momentum that carries.
Kirk set the benchmark and is what many of us saw first, and his enthusiasm and humanity and intense engagement with everything was inspiring.
Plus, what are the only true and indisputable Star Trek Captain rankings?
That said, I shall now definitively prove that your rankings are incorrect* and that a True and Accurate answer is as follows:
*for certain meanings of "incorrect"
Starting from this list, I will add only one, who is one of the several captains in DIS, who has a complete story arc (spoilers for Discovery follow):
Most of what follows is true.That leaves us with the following-
TOS: Captain James Tiberius Kirk ("Kirk")
TNG: Captain Jean-Luc Picard ("Picard")
DS9: Captain Benjamin Sisko ("Sisko")
VOY: Captain Kathryn Janeway ("Janeway")
ENT: Captain Jonathan Archer ("Archer")
6. Kirk (TOS). Undeniably adventurous, Kirk is the worst captain we've seen. Things always become personal, rules are there to be broken, cultures to be victimized for immediate gratification, crewmen to be sacrificed to avoid the need for careful planning. He's all id. There's no doubt he was successful, but he's not the captain any starfleet graduate should aspire to be. In the first episode, he oversees the destruction of an alien race; he'd have been killed in the second episode by a teenager if he had not been rescued by a more competent captain, in the third episode he falsifies a service record of a friend; etc....
5. Sisko (DS9). To be fair, Sisko probably is responsible for more deaths than Kirk, because he starts the war with the Dominion, which kills a billion or more sentient beings. Most are Cardassians, so perhaps that doesn't matter to you or the Federation, but as a body count it's impressive for a captain of a ship that doesn't move anywhere. Taking a cue from Kirk, he actively manipulates a planet's culture and becomes a religious icon for the Bajorans. He at least struggles with the tension and divided loyalties of being a prophet and being a captain, which shows us he knows he's no good.
4. Picard (TNG). Completely competent as a captain. A little too excited in the first season to separate the families in the saucer section from the actual protection the ship he is in charge of can offer, Picard knows how to lead and how to defer to expertise, when he's not on the holodeck or being a mouthpiece for genocidal space robots.
3. Janeway (VOY). Extraordinary circumstances can make a hero, as Janeway shows. Cast into a distant sector, her return to the Alpha quadrant led to First Contact with so many species, which she accomplished (in a way Kirk did not) conscious of the regulation and expectations of a Starfleet captain.
2. Archer (ENT). Weak writing in the first two seasons mean this series starts with so many dogs that it's surprising it got renewed. However, ENT season 3 gives the Xindi arc which combines the distant-quadrant arc of VOY with an immediate threat to Earth. Archer brings his ship home and saves our planet. He has a dog and plays waterpolo -- a much deeper character than you suggest, I tellz ya, and a detail we never saw in action, though it was said so many times, proving the screenwriting maxim of "Tell, don't Show". ENT season 4 (with a new showrunner who IIRC is not a waterpolo fan) gave a number of stories about the foundation of the Federation. Each was 2-3 episodes, and revisited something from TOS, but with greater scope for character development. Archer isn't the focus of all of these stories -- as is right since he's a captain -- but the stories provide origins for so much of what we see as definitional for the Federation, that we can claim Archer's understanding of captaincy was crucial to the formation of what a Starfleet Captain should be.
1. Captain Christopher Pike (DIS season 2, SNW). The first captain of the Enterprise we met, returned and was given a rich story in DIS season 2, that showed leadership and humanity within the frame of the Federation's rules. Never has there been a captain that balances caring for his crew with the burden of his position. On top of that, he is acting with a certain knowledge of his own future (which viewers of the original pilot/TOS's "The Cage" know as the earliest presentation of any captain to be true), which means his self-sacrifice, rescuing others at intense personal cost, is unparalleled for any Star Trek Captain. Pike's story arc unfolds operates with the inevitability of a Sophoclean tragedy.
(And now we will get a series with him.)