When I wrote this tool my main purpose was to know where to create my VMs to have a reasonable latency to other services. In my case reasonable means < 100ms. This will definitly vary across products. As for the asymetric results you are absolutely right in fact if you look at the chart in the site the roundtrip fron A to B and B to A are different, which is typical in cloud environments.
I try very hard to emphasise on latency and not throughput, in fact I don't think I mention throughput at all since it adds another layer of complexity.
As for ICMP vs TCP/IP or any other layer 3/4 protocol it's just a matter of time. If this becomes a topic of conversation often I might end up extending the service to support "custom" packets.