Xeyes was occasionally useful for telling you when the machine it's running on has gone down or is too overloaded to be usable. In today's world of nested window systems it's also helpful for telling you if your mouse cursor movement is being delivered to a nested screen.

Mostly, though, xeyes was "pointless" in the same sense that fine art is "pointless", like xneko, window manager themes, xshostakovich, or screensavers. It doesn't have a point; it is itself the point.