You don't have to "blow things up" to train an AI for ATC.
Tesla's FSD computer, the one in each car, is calculating a driving solution all the time, even when Autopilot is not engaged. When the human driver's actions diverge significantly from FSD's solution, the data is sent back to Tesla and, when the human's performance was better than FSD, is used for AI training.
That is one way that an ATC AI would be trained.
One way in which FSD has an advantage over human drivers is that it is watching all eight exterior cameras simultaneously without ever being distracted or having to "turn its head" in different directions to see all necessary angles. The ATC AI would have a similar advantage in that it would have more information available to it than any single controller now has.
For example, it would know about all of the other airplanes currently flying toward a particular STAR and at what time they will reach each waypoint. Airplanes hundreds of miles apart can be sequenced and deconflicted hours before they arrive at the conflict point creating a more efficient system, with fewer bottlenecks, than is currently possible.
FSD has a features with some parallels to this sequencing in its navigation software. FSD knows when you will need to charge and what Superchargers are available along your route in the area where you will be ready to charge. It also knows how many stalls are available at each charging site, how many other cars are navigating to those chargers, and at what times they will all arrive. It uses this data to spread the charging demand across the stations to avoid anyone having to wait for a charger.