ICMP is a different path
I used to quote ping as if it were the round trip of the application. Then a host that answered ICMP in 180 ms opened TCP in 240 ms, and a host that dropped every ping still completed a TLS handshake. The ICMP reply had been policy-routed, rate-limited, or generated by something that was not the process I cared about.
When I need a number I can stand behind, I time the SYN-ACK, or the first application byte, on the same five-tuple the work will use. Ping stays useful as a reachability check. It is not a latency budget.