I think you're confusing Ingresses and Ingress Controllers? Traefik/HAProxy/Nginx act as Ingress Controllers, not Ingresses. Ingresses are the objects created by users to define an intent of L7 traffic forwarding/ingress. Or maybe I'm misparsing your post.

Anyway - the reason K3s can come with an Ingress Controller OOTB is purely a result of the fact that K8s has made it possible by making the architecture pluggable. Nearly every K8s-a-a-S solution comes with its own built-in flavour of an Ingress Controller (and other controllers, too). K3s is just such an implementation. K8s could come with its own standard implementation of an Ingress Controller, but considering how much the implementation varies between deployments, it makes sense they have opted out of that.

Comparing K8s to K8s distributions (like K3s) is somewhat missing the point of what K8s is - a framework to build your own implementation upon, with whatever fits your deployment.