Unless your entire Internet usage is PPP LCP confined to A&A's network it's not more accurate. It's also not as simple as 'ICMP is lower priority'. On carrier grade routers with distributed packet processing and ASICs, so not Firebricks, ICMP to the router may be handled differently, ICMP through it is not.
CQM is not representative of user experience end to end it's a tool to diagnose potential issues across access network and backhaul between customer and LNS.
Surely CQM proves there is no issue between the router and the ISP, which is the point?
If latency is elsewhere on the network its almost certainly not within AAISP so nothing they can do about it.
The problem is like you said, if your own router is slow to respond to ICMP then ping packets timing out would indicate latency that would not exist for normal traffic.
Another pitfall can be if you setup a DMZ, ICMP will get translated over NAT to the target machine, rather than being replied to via the router. I learned that the hard way.
Quote from MrSaffron themselves:
Each pixel is 100 seconds, so yellow may be just 1 or 2 samples (1/second) having higher latency, i.e. if the thin blue line does not move then what you have is jitter and this can be caused by simply loading a web page.
I've not had a jitter-free connection in years yet its clearly not my ISP as there are Zen users on various technologies in the
BQM forum post with very different graphs.
My connection is never idle though, I have Wireguard, OpenVPN, pfSense pinging various servers for its gateway monitoring and plenty of port scans, web server and SSH attack attempts being blocked at the router. Also with multi-wan the firewall gets restarted whenever one of the mobile connections latency gets too high, more often than I'd like, which will temporarily kill response on all WANs. None of this is down to ISP issues.