It is incredibly important to whether the US can maintain its AI lead. If foreign competition is closing the gap only by distillation, then the frontier labs can focus on preventing distillation and maintain their lead that way.

US dominance is also important for approaches to safety, especially political approaches. If the frontier models are all US-based, safety might be tackled via internal US policy. If other countries can independently train competitive models, international cooperation is required.

Edit: It is also important for the business model. Companies won't be able to justify tremendous training costs if competitors can replicate their product much more cheaply via distillation.