A different regulation (applicable only to radar environments, which AUS is) allows for a departure if an arriving aircraft is 2+ miles away from the runway, as long as there is at least 3 miles of separation within 1 min after takeoff.
All that being said -- it is possible to execute a squeeze play like this if everything is perfect, but you need the departure to go IMMEDIATELY. Trying this in low visibility was extremely reckless and incompetent.
In the linked communication you can see that he knew both planes were incoming on the same runway and confirmed his brain dead plan repeatedly to both crews. Even telling SW that they could take off because Fedex was 3 miles out. At any reasonable speed this is virtually no time. At 165 it would be a little over 1 minute. Since the critical moment came around the 2 minute mark it seems likely that in addition to any other faults he also can't estimate distance.
Even after it went south or shall we say southwest he was never capable of recovering in any timely fashion as evidenced by the Fedex crew taking over his job. As a result of his incompetence everyone would have died. The only meaningful fact he could have ascertained in order to correct his plan would have been to understand that planes go fast. At this juncture retraining him seems like a poor decision. He's a hazard.
Let's assume that you are right. I don't think I can be as confident about anything as you are. Especially not before an investigation, but let's pretend that you are right: the controller in question is an imbecile who need to be fired immediately.
How is that not a process problem? How did an idiot get on frequency controlling traffic at a big airport? Shouldn't there be filters to prevent that? And if he is an idiot, which I don't believe but we are in a hypothetical, how many others there are?
If you see r/ATC, he's been shuffled between locations and this isn't his first screw-up. He manages to stay employed through claiming discrimination under EEO when performance issues come up. There's even another past incident from another airport featuring him.
Luckily, this may be the nail in the coffin that even US Critical Race Theory policies can't prevent, and it happened without any loss of life.
From the responses of those who have worked ATC, lazy & incompetent would be more accurate than idiot. He sounds checked out, and isn't really thinking about his choices.
They're notoriously awful for not firing people who repeatedly put lives at risk.
Additionally, assuming you're American, would you apply this same logic to police officers? ATC is similar in that lives are at stake.
The same system should definitely exist in law enforcement, to the extent that the mistakes are made in good faith. I would argue that a good percentage of the “mistakes” made by police in the US are malicious in nature, akin to ATC intentionally putting planes in danger. Our law enforcement culture in the US is so rotten that mistakes are neither punished nor understood.
To your point that ATC is notoriously awful for not firing people, I would say their safety record speaks for itself. The impulse for punitive vengeance is what puts lives at risk, not ATC's safety culture.
A very pertinent one. The comment you responded to talked about how aviation achieves their stellar safety record. You told us that in your other industry (now we know it is mining) things are done differently. So it is fair to ask: How is that going for you? What are the results? Are you safer or less safe than aviation?