The obvious assumed premise of this argument is that Anthropic are actually on the path toward creating super-intelligent AGI. Many people, including myself, are skeptical of this. (In fact I would go farther - in my opinion, cosplaying as though their AI is so intelligent that it's dangerous has become a marketing campaign for Anthropic, and their rhetoric around this topic should usually be taken with a grain of salt.)
LLMs allow hostile actors to do wide-scale damage to society by significantly decreasing the marginal cost and increasing the ease of spreading misinformation, propaganda, and other fake content. While this was already possible before, it required creating large troll farms of real people, semi-specialized skills like photoshop, etc. I personally don't believe that AGI/ASI is possible through LLMs, but if you do that would magnify the potential damage tenfold.
Closed-weight LLMs can be controlled to prevent or at least reduce the harmful actions they are used for. Even if you don't trust Anthropic to do this alone, they are a large company beholden to the law and the government can audit their performance. A criminal or hostile nation state downloading an open weight LLM is not going to care about the law.
This would not be a particularly novel idea - a similar reality is already true of other products and services that can be used to do widespread harm. Google "Invention Secrecy Act".
Also, your comment is a bit presumptuous. I think society has been way too accepting of relying on services behind an online API, and it usually does not benefit the consumer.
I just think it's really dumb that people argue passionately about open weight LLMs without even mentioning the risks.