The most interesting security bugs have causes that are spread across large codebases, or networks of dependencies.
Training the AI to "output secure code" won't work if it doesn't also have access to the source code of every dependency that it's using... and even then, given current model speeds and prices most developers won't want to wait for an hour on every edit they make while the LLM reasons through all of the dependencies.
Vulnerability discovery has essentially moved to a "proof of work" computation model with AI that has some similarities to crypto like BTC or ethereum 1.0. I don't see any reason a well funded adversary couldn't use this same process on open-source code to develop exploits. I'm sure AI would be happy to try and create exploits from the results rather than fixes.
This sort of proof of work has a notable difference from crypto in the asymmetric nature of what each side is targeting. In crypto, each miner was attempting to find a solution to the same problem and they would all move on to a new one once a solution is found. However with AI vulnerability scanning, the non-deterministic nature means an adversary is likely to find different vulnerabilities. Even if it doesn't, the adversaries have a different post-discovery workflow (i.e. probably less compute intensive aka cheaper due to only needing one viable exploit to win) than the software maintainers do.
Considering it's possible both the adversary and their target could both do all this while running Claude puts Anthropic in a real "Merchant of Death" position.
The goal of AI-generated code should not be that one needs a AI-based security review tool on top of it, but that the AI-generated code in itself is reasonably secure.