It would make sense that the captain of the Enterprise is known the same way a General Norman Schwarzkopf or General David Petraeus is known and former captains of the Enterprise might be well known to history buffs the way history buffs know American Civil War generals.
But how many people remember Civil War Colonels?
Out of the naval heroes of the Civil War, it's Admiral Farragut, in command of a big formation of ships, that people generally recognize. In WWII, the names of Captains seldom register even among history buffs, it once again being the Admirals that are remembered.
If Kirk and Picard made it, was it because starships of the Trek future are categorically different beasts from today's naval vessels (so Kirk gets fame or infamy the same way a submarine skipper got it, by boldly representing an exotic and exciting branch of the military)? Or was it because they were so exceptionally good at their otherwise humdrum jobs (so Kirk is remembered because his feats rival Stephen Decatur's)?
Really, even the most heroic naval achievements in Earth's wars are often associated with ships rather than commanding officers. Many may remember the Jervis Bay, but who would know of Edward Fegen without googling? Is any of the captains who sunk the Bismarck remembered in any fashion? Does anybody remember who captained the Bismarck?
Timo Saloniemi