Ususally it's trivial installing curl, it's one command and a few seconds if your container has internet connection. And even if it does not you can just host the binary somewhere you container has access to.
Usually people prefer to have smaller containers vs large one with "potentially useful tools", and of course if one would like to create an image based on traefik and add tooling that they require in it, they can do so.
I'm glad that ping helped you, however just today I wrote about the ping the following post, so your milage may wary.