I've never used Claude or anything like it so this may be a dumb question: could you solve this problem by having a CLAUDE.md file that simply says to use AGENT.md if one is available. Can an AI agent not do that?

Yes, the most common solution for this problem either creating a symbolic CLAUDE.md link pointing to AGENT.md (or visa versa) if OS supports it.

Or, in CLAUDE.md have an instruction to follow AGENT.md - but this approach is quite unreliable.

These are solutions to a problem that shouldn’t exist in the first place. How else can one explain Anthropic’s reluctance to adhere to a widely adopted standard, if not as an attempt to build a walled garden around an otherwise great product?