Also, Kruge was a spymaster of some sort; he'd probably have more use for a "management center" than most Klingon skippers, and less reason to lead the ship from its navigation bridge.
As for recordings that have more dramatic flair than today's cctv imagery... That is only to be expected. It reminds me of the problem people have with doors that only open when the character really
wants to step through, rather than every time he happens to approach the doors. It's a feature the user would want
the doors to have, and easy enough to implement with a fairly idiotic computer program that monitors the movements of the character - but people still think it's "wrong" because it doesn't work like 1950s vintage automated mall doors.
Whenever we see "cctv footage" in Star Trek, it's presented for dramatic purposes: in a courtroom or the like. Naturally, it would be edited for dramatic impact - either by a human(oid) user beforehand, or then by a marginally smart computer program in real time. That's a desirable feature, and something technology can fairly easily provide, so its absence would be more curious than its presence.