TOS often had sequences when Kirk communicated with admirals over subspace.
I think that "phone an admiral" sequences could be fun, if they were done with self-awareness.
Mission: Impossible always (or pretty much always) started out with a taped briefing. The catch phrase "Your mission, should you choose to accept it...." made that amusing and entertaining.
I'm not suggesting exactly that, but if the writers are aware that "phone an admiral" sequences are clichés (they are) and bring some twists to the table with that in mind, so the sequences are not intended simply to play straight or are otherwise infused with some entertaining novelty, it might be effective.
TNG managed to pull that sort of thing off, or at least make a good try, on at least two occasions: for example, with the "Captain Picard Day" scene in "The Pegasus," when Picard had that banner hanging in the background while he talked to Admiral Blackwell, and in the film INS, when Picard had the ridiculous thing on his head while he talked to Admiral Dougherty (with the added twist that that "phone call" served to introduce one of the film's villains).
In "Lolani," the Commodore Gray sequence was a cameo sequence for Erin Gray with the well-executed novelty of having her wear an implied but never-before-seen costume for female Starbase command personnel. Those factors probably aren't enough to bring freshness to the trope, but they might be considered efforts in that regard.
