I won't lie, this sounds like a recipe for context rot.
LLMs degrade as the context / prompt size grow. For that reason I don't even use a CLAUDE.md at all.
There are very few bits that I do need to routinely repeat, because those are captured by linters/tests, or prevented by subdividing the tasks in small-enough chunks.
Maybe at times I wish I could quickly add some frequently used text to prompts (e.g. "iterate using `make test TEST=foo`"), but otherwise I don't want to delegate context/prompt building to an AI - it would quickly snowball.