It can try its own file and fall back to generic like here. What's wrong with that?
Wasting turns? That is silly, use a better harness. Also token usage can mitigated by incremental discovery instead of stuck 5k+ worth of tokens in the AGENT/Claude md file.
Every turn means more tokens in ways that are not obvious to most people and lead to tons of unnecessary cache reads.
No harness can batch your agents.md read with the reads the contents of the file tell it to read.