Hence, my earlier thought that it might not be a good idea to name ships after battles. That's all I'm sayin'.
While it was Roddenberry's intention to have a more international name with "Enterprise" I wouldn't be surprised if he also had similar thoughts that made him decide to drop "Yorktown".
While the names are admittedly Earth-centric most are derived from sailing ships. Since Vulcan doesn't have oceans for ships to sail on, it didn't have any ship names to suggest.
But how many times did the Enterprise
or one of her sister ships actually conduct "first contact" in TOS?
Often there had been other ships before doing that like the Archon,
or the Valiant.
For all we know the starships with the militaristic names may have mostly been assigned for patrol duty but not deep-space exploration.
However I can't help myself to imagine this scene from an alternate scripted version of "The Omega Glory":
"I'm Captain Ronald Tracey of the USS Constitution
, I've come in peace"
"Cursed Yang! He is using the blasphemous words of the Yangs, chop his head off, rightaway!!!"