What the government would have that public research would not is a) better quality training data (they have direct surveillance at the telco hardware level, not just what’s publicly scrapeable) and b) less need to artificially limit the AI so end users can’t abuse it.
I’d also disagree on the leaked NSA stuff being only “good”. Russia used it after it leaked to unleash the NotPetya malware, and that was the most damaging malware of all time.