Because you're better able to take over the codebase a local model wrote than one Claude wrote? The original question was about taking over an LLM-written codebase, it doesn't sound to me like the argument was about a codebase that Claude, specifically, wrote.
What does it matter what the codebase is made with? If Claude is down, use Codex, or Gemini, or Deepseek. That version of the argument is just way too easy to counter.