By itself, this is uncharacteristically dystopian for Star Trek because it suggests people will relax so much less that arm rests are unnecessary. Strange because Star Trek usually presents a more optimistic picture of the future.
That futuristic look is more important.
I mean, there's an entire TNG episode about how Picard begrudgingly takes a vacation on the tropical "pleasure planet" of Risa and is completely miserable until he gets caught up in a wacky Indiana Jones type adventure. And an entire DS9 episode where Worf goes to Risa and decides he'd rather help some nutjobs sabotage the weather control system. These are not people who like to relax!
Or they relax SO often, that they don't need arm rests (because their arms are never tired, because they aren't working much)
Starfleet, despite the ranks, authority structure, style of discipline, use of “courts-martial”, and the fact it fights wars, is not, as Starfleet personnel are eager to point out, a military force. Also, usually, Starfleet doesn't run diplomacy, they provide transport for diplomats.
They do sometimes fill in when the transported diplomats become unavailable, when an emergent needs happens without time to dispatch a diplomat, or when an individual Starfleet officer is requested by tbe parties to a dispute (where the Federation is a neutral mediator) or the other party (where the Federation is a party), but all of those are implicitly exceptional events that disproportionately happen to the particular officers on whom the franchise focuses.
Regarding diplomacy:
- Kithomer Accords, re-established between Cpt. Sisko and Chancellor Gowron, the first accords were Picard's job (could be wrong about that)
- everything Bajor related, despite the planet being the most strategic important one in the Alpha Quadrant there was never an official embassy mentioned, everything was run by Sisko
- the Alliance with the Romulans during the Dominion war, again by Sisko and this Admiral
- the ultimate peace treaty between the Dominion and the Federation
- every first contact mission (understandable, Starfleet is the exploration arm of the Federation with a clear charter here) but also every follow-up mission (see Lower Decks)
Just from top of my head, all major diplomatic treaties have been negotiated by Starfleet personell. In a sensey Starfleet is a state-within-a-state, running crucial functions of the larger state with little to no oversight.
Everything not shown on screen, or explained / hinted at, is not necessarily canon.