There are certainly types of data that are already prohibited for export and dissemination. In this case, I would argue no new law is needed, the existing laws

There are certainly types of data that are already prohibited for export and dissemination. In this case, I would argue no new law is needed, the existing laws cover the export or dissemination of dual use technologies. If the LLM becomes dual-use/export-restricted/etc because it was trained on export-restricted/sensitive/etc data, it is already illegal to disseminate it. Enforce the existing law, rather than use taxpayer money to ban and police private LLM training because this might happen.