Most people run these on cloud VMs, which works but has a cost and privacy ceiling. The natural alternative is a low-power always-on device at home (think: the RPi homelab crowd, but for AI agents). 15W idle draws running 24/7 cost less than $20/year in electricity.
The naming actually clarifies the hardware requirement in a way "agent" didn't - an agent can be stateless and batch-triggered, but a claw needs to be persistently reachable. That's a different design constraint. Would be curious if anyone's run into issues with consumer ISPs blocking inbound connections for claw-style setups.