Besides, as famous as Kirk was, he still was no Founding Father of the Federation. I don't think people in-universe worship Kirk or hold him up on as high a pedestal as do many people in the real world.
I like to think that as well. Though, admittedly, Kirk did play a key role in saving the Earth from destruction by an unstoppable alien probe twice
in the span of a dozen years or so, which does seem to be the sort of thing that would get someone a pretty sizeable mention in the history books.
And on top of his contributions to Federation science, diplomacy, and defense while in command of the original Enterprise
's five-year mission, he also uncovered and thwarted a Klingon attempt to steal the secrets of Project Genesis, and he personally saved the Federation President from assassination and prevented the Khitomer Conspiracy from instigating a war between the UFP and the Klingon Empire.
I doubt that Kirk would be worshipped, but I imagine that he would be held in at least as high a regard as we today tend to hold leaders like Ulysses S. Grant, Dwight D. Eisenhower, Chester Nimitz, or Douglas MacArthur.
I'm sure Kirk isn't venerated, and he certainly has his detractors. But the idea that he would be remembered and respected enough for Starfleet to name a ship U.S.S. James T. Kirk
is completely plausible.
If anything, the relative dearth of starships named after people from the Federation's 200-year history is somewhat implausible. Realistically, they'd probably be naming a significant percentage of their starships after well-regarded Federates from their own history -- to say nothing of naming more ships after people and places other than Earth -- instead of naming so many ships after Humans and Earth locations from the 19th and 20th centuries.