I prefer flexible companies that allow you to use whatever software you want with their services.
OpenClaw heartbeats (essentially idling) could cost single-digit dollar amounts of LLM inference per day, _before any actual user activity_. Another example was IIRC the Pi agent harness sending a new timestamp at the start of every message turn (which sends along the entire chat + tool call history up until that point as context), which of course also invalidates the cache's hash, causing effectively unnecessary re-compute.
I'm not defending Anthropic per se, but just try to picture yourself in their position as a company desperately strapped for any amount of free compute trying to scale up every service as aggressively as they want/have to… And the caching topics are just one potential issue that could occur with "third-party" software. Not that I like it, but of course they'd be quick to ban such behavior in favor of first-party, "guaranteed behaving" customers.