The problem is pinging 1.1.1.1 can end up hitting a really really close-by server. You could be having ISP issues and 1.1.1.1 could end up being closer to you than the issue is, so you get okay ping results but still unable to access resources on the other side of the issue
Most of my connection issues are between the street and my computer, I don't think Cloudflare got there. Yet.
You can have routing issues that alow some IP addresses to work and others not, anycast or not. It's not supposed to be a comprehensive connectivity report, just a sanity check that the intertubes are connected at all.
You're thinking far too hard. If I can ping 1.1.1.1, it means traffic is flowing from inside my network, to outside my network. I'm not going to diagnose my ISP's issues, that's their job, I just need to know that it's not my problem.