How would this destroy Anthropic, exactly?

Not just Anthropic, but practically speaking, the leading foundational model labs like Anthropic and OpenAI are burning through enormous amounts of money, and will need to pay that money back. If they are designated as supply chain risks, or controlled technologies, their ability to achieve that ROI is severely constrained.

They are not turning a profit, and aside from enterprise token billing, every other offering they have is a loss leader. In order to flip that around they need to drive down the cost of inference significantly, either through massive compute improvements, more efficient or lower cost models, and either one lowers the barrier to entry for local and/or private cloud inference for open models. The moat established by the expertise in model training is effectively dissolving as they approach recursive self improvement because any mechanism that prevents model distillation effectively reduces the quality and utility of the models, so each improved model makes their competitors better by default if they want to realize those gains.

The reason for the pivot to control and regulation seems to be more about erecting an artificial moat in their market, and having these technologies controlled or highlighted as supply chain risks will continue to drive investments in alternatives, especially in other countries where data sovereignty and domestic tech has become a priority given the last decade of the US dominated tech industry.

I don't think that AI is going to go away, but I think the future of AI in the next several years looks alot like massive overfunded foundational model providers collapsing, their employees launching dozens or hundreds of direct competitors, and the leading hyperscalers buying up datacenter capacity the way they bought up dark fiber 20 years ago.