Rootless exists in Docker, yes, but as OP said, it's not first-class. The setup process is clunky, things break more often. In podman it just works, and podman is leading with features like quadlets, which make docker services just services like any other.
That page does not address rootless Docker, which can be installed (not just run) without root, so it would not have the ability to clobber firewall rules.