And while Kirk was famous in his time and canonically had at least some of his adventures taught at the Academy, that doesn't necessarily mean that people would know about Uhura, Sulu, Scotty and Chekov.
This is exactly my point. Many people may know a little about famous military people from our own history, whether Washington, Grant, Pershing, Eisenhower, Patton, heck even Stormin' Norman Schwartzkopf.
But how many of the members of those figures' senior staff do we know about? How many of those people can even people with above average education actually name? Other than Alexander Hamilton, I'm guessing zero.
Archer, Kirk, Sulu, Picard, Sisko....these are names that will definitely find their place in history books. But Crusher, LaForge, Troi, Scott, McCoy, Dax? Nope.
There's plenty of canonical evidence to support the fact that supporting Trek characters, especially supporting ones, are not, in fact, treated like celebrities or royalty in universe.
No one seems to recognize or had heart of Scotty in "Relics", though Picard expresses interest in hearing his insights about the "events" of his time. Not even his actual accomplishments, just things that happened while he was alive.
Bashir doesn't recognize Data on sight in "Birthright", but has heard of him, as the only "synthetic lifeform" in Starfleet is obviously going to be something most people have at least heard of. But he's not so famous that Bashir instantly knows who he is. Guess he was never on the cover of Space Vogue.
In "Defiant", Dax and Kira aren't exactly fan girl squealing about Riker being aboard the station. Dax doesn't say, "OMG, you met Riker! WOW, he's famous!" She just smiles and says, "Oh, I met Riker once last year." Big whoop.
No one seems interested or even aware that Admiral McCoy is touring the Ent-D in "Farpoint."
Sisko and Dax DO geek out about Kirk on "Tribble-ations", but because he's the actual captain. Sisko struggles to remember who McCoy is/was. It tracks that Sisko, who clearly idolizes the old Enterprise, would be familiar with the names of Kirk's crew, but he hardly reacts to McCoy's presence with anything other than a shrug.
Other members of the crew notably mistake Kirk for someone else in the bar scene, not even knowing what he looks like.