That’s not true:

> By default containers are unprivileged […]

https://linuxcontainers.org/lxd/docs/master/security/#contai...

As for LXC:

> LXC containers can be of two kinds:

> - Privileged containers

> - Unprivileged containers

> […]

> The latter has been introduced back in LXC 1.0 (February 2014) […]

https://linuxcontainers.org/lxc/security/

It can do both. https://linuxcontainers.org/lxc/security/

I have always used it for unprivileged containers, and I remember using it as such in 2016. IIRC both podman and rootless docker are much more recent.