Punishment isn't a problem because it doesn't work. If you create a system that lulls people into a sense of security, no punishment will stop them because they aren't doing it thinking "it's worth the risk", it's that they don't see the risk. There are so many examples of this, it's weird people still think this actually works.
Furthermore, it becomes a liability-washing tool: companies will tell employees they have to take the time to check things, but then not give them the time required to actually check everything, and then blame employees when they do the only thing they can: let stuff slip.
If you want to use LLMs for this kind of thing, you need to create systems around them that make it hard to make the mistakes. As an example (obviously not a complete solution, just one part): if they cite a source, there should be a mandated automatic check that goes to that source, validates it exists, and that the cited text is actually there, not using LLMs. Exact solutions will vary based on the specific use case.
An example from outside LLMs: we told users they should check the URL bar as a solution to phishing. In theory a user could always make sure they were on the right page and stop attacks. In practice people were always going to slip up. The correct solution was automated tooling that validates the URL (e.g: password managers, passkeys).