To be honest, I wouldnīt read much into the high back of the chair. I mean, why reserve this higher back for flag officers? What possible advantage can it bring? More comfort? Maybe. But why deprive the Captains of this privilege? They spend much more time sitting in it on their 5-year-missions, than flag officers do during the occasional war game. Other than more comfort I canīt really see any other advantage to this type of chair. On the contrary, you canīt even see whatīs going on behind you! Wesley always has to swivel his chair around when addressing someone at a console there, he canīt just look over his shoulder.
Finally, the crew will know, when their ship is commanded by a flag officer, they wonīt need a different chair to visually remind them of that
IMO itīs just the personal preference of the Lexington
īs CO. Other than that, I canīt come up with an explanation that makes sense in-universe.