I'm pretty sure it supports ICMP, as TCP/IP cannot work properly without it. I guess you mean ICMP echo. Also there are like four kind of Azure load balancers and this is only true for some of them.

I can ping bing.com, but does that mean bing is not hosted on Azure? [Though it redirects to pinging something like a-0001.a-msedge.net]

It may just not use the Azure LB service (e.g. running HAProxy on virtual machines instead).