No we wouldn't see improvement in security, because you're judging this case on a few isolated facts. If you think about the sort of work that an intelligence wing will be dealing with, then everyday, all day the hierarchy are having to make judgement calls on the basis of limited and unproven data, as well as all the drudgery of running any complicated organisation. Seen in hindsight and stripped of context it's a black and white case. In reality management will have been worrying about their intelligence "assets", whether they've been turned, whether incoming intel is fact or fiction, diversion or substance, what if anything merits escalation higher up the food chain, dealing with mundane workplace, management and leadership issues, that Airman A is accused of harassing Airman B, that the West Texas control room gets too hot because the air con doesn't work properly, that some civilian jerk is trying to hack or DDoS the units computers, dealing with staff hiring, training etc etc etc.
Maybe 102IW did have a bad culture and lax security. Or maybe they were reasonably competently run with a few mistakes (which I'll wager all intel organisations have) and their brass have simply been hung out to dry, partly so the Pentagon are seen to be doing something, partly as petty politics within the ranks. Either way we'll never know.
If firing or reassigning the entire command chain were the norm, then what we will see is thorough attempts by the entire hierarchy to cover up misdemeanours. Arguably would have been very difficult in Teixeira's case as he was caught from the outside, but in a total blame culture, all the prior evidence within 102IW would have been carefully destroyed, and after the event nobody would admit anything.