The real issue is that API providers log everything. OpenAI/Anthropic already capture full CoT traces in their logs — they just don't expose them. Distillation via API is just making explicit what they already have.
The whole point of the encrypted payload returned to the client for future re-submission would be that they don't log.
The whole point of the encrypted payload returned to the client for future re-submission would be that they don't log.