Yes, I agree, the characters are using these skills when your scenarios arise. But, half the time these are roleplayed out and my players have the common sense not to insult their Captain. As for Culture, to me, not useful. As for your other scenarios:
Diplomatic functions = Diplomacy. Good skill and characters have purchased it.
Ferengi Rules of Acquistions = Culture probably and if my characters don't buy it, they don't know them.
Visiting home = World Knowledge. But, I'm not going to have my characters makes rolls for possible hazards around their home planet they should know. Just my opinion.
Recalling famous incidents = History. But, characters can research this using computers too.
My opinion is the World Knowledge and Culture skills for the characters own home planet were just wasted skills. But, to each their own.
IMHO (not to suggest I'm right or anything !) I agree with Dan...I think Culture, History, Language & World Knowledge are core skills for a species. I include them in any species template I dream up...maybe you won't ever need to roll them, although I think with creative adventures it can come up. More than anything these represent the combined knowledge someone has just from being raised. I don't see how it isn't feasible to have ratings in several cultures. Take the present day...I may have Culture (North America) 1 (2)...fair bit of knowledge for my hemisphere...lesser, but still some for others...maybe Asia is of interest & I've studied it, good reason to use the 1 for a roll. In a galactic setting it's just a grander scale simply because no one has to be limited to just one planet.
I also agree -- those are core RP skills. That's why I make characters start with, at the absolute minimum, the Species Template to get these necessary skills. From there they can spend DP if they'd like.
I reference them at least once an episode for my players.
I allow players to use the overlays as guides but expect them to spend the DPs on skills they want or need for the type of character they want to play.
In my campaign you can switch positions or careers so long as you have the minimum skills called for in the overlay.
Recently a helmsman was promoted to security chief because he had the know-how needed. The player XO suggested him to me as a replacement and we approached the player who quickly accepted.
He had enough points in phaser, unarmed combat, weapons systems and defector systems skills and engineering skills but lacked the security and small unit tactics but that needed for the job. This was fixed by NPC captain offering the officer the position but noting he would have to attend a security training course to prepare him for new job.
This is a good player who I could easily taking on more responsibilities and maybe even serving as an XO in the future if needed, his character would be given the opportunity to train for that just as any player could have his character switch jobs to a more challenging role on board the ship.
This isn't D&D, character skills make the job, not the template.