Yes, but even rootless containers rely on user namespaces, which are a recurring source of privilege escalation vulnerabilities in Linux.
The issue of root vs rootless is unrelated to escaping the container. User namespaces lead to privescs because attackers who can enter a namespace and become the root within that namespace have access to kernel functionality that is far less hardened (because upstream has never considered root->kernel to be a privesc and, of course, most people focus on unprivileged user -> kernel privesc). The daemon running as root doesn't change anything there
No, it's because the malware would have direct access to the (privileged) Linux Kernel via system calls.