>"Everybody is talking about clock accuracy and totally missing that devices in the middle of the network path do not care about responding quickly to pings. Middle devices are generally routers or firewalls, and their job is to route and firewall, not to respond to a packet as quickly as it comes in."

That's not correct. A box in the middle of the network path by definition doesn't respond at all to the ping request since it's not addressed to them. It's simply forwards the IP packet that encapsulates the ICMP echo request towards its destination. As forwarding happens in the data plane this doesn't involve the control plane at all. A router with no QoS will forward IP datagrams at the same rate whether they encapsulate TCP, UDP or ICMP.