To be honest, I wouldn´t 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 can´t really see any other advantage to this type of chair. On the contrary, you can´t even see what´s going on behind you! Wesley always has to swivel his chair around when addressing someone at a console there, he can´t just look over his shoulder.
Finally, the crew will know, when their ship is commanded by a flag officer, they won´t need a different chair to visually remind them of that
IMO it´s just the personal preference of the Lexington´s CO. Other than that, I can´t come up with an explanation that makes sense in-universe.
Mario
While we can speculate on what the 'dramatic' purpose was, the actual real life production purpose is that they wanted to make the Lexington's bridge look different than the Enterprise's... the same reason they changed the screen panels above the communications and science stations to make them different than the Enterprise's.