The obvious reason is that they would prefer to have CLAUDE.md files in every repo (even if it's just a symlink to AGENTS.md). It serves as a free advertisement for them. Same reason as for auto-adding attribution text in commit messages, etc. It's the "Sent from my iPhone" of our time.
Except I actively despise that commit message anytime I see it.
While I agree with your analysis, I think Hanlon’s razor applies here – CLAUDE.md has probably just been hardcoded, the same way “master” used to be the hardcoded default in Git. If it was for advertising, Claude would equally recognize CLAUDE.adoc, CLAUDE.txt or CLAUDE files.
I think it's more than that. They truly believe Claude Code to be a moat (both the harness and the posttraining) to be a moat.
I've been deeply distrustful of Anthropic from early early days. They have always been openly disdainful of user feedback. I would not be surprised if later they try to implement more shenanigans to keep people locked into CC.