Why is pinging an anycast address an issue? Most people, myself included, ping addresses like 1.1.1.1 to check for internet connectivity. It's a perfectly valid check, you don't need a fine grained test all the time. If it fails, then I go looking in detail. Most of the time it will pass.
Pinging a domain name could fail for a variety of other reasons, particularly if it's not a reliable site. Cloudflare's business is being reliable; few sites would be a better choice.