Podman doesn't have a dependency on systemd. e.g. it is packaged in Void Linux.

Podman has a better architecture than Docker in that it can easily run on a non-privileged user.

Quadlet (aka podman-systemd.unit) is a podman-systemd integration which can make it easy to launch and orchestrate podman containers via systemd. You can get all if the systemd dependency handling, require other units to run after a container finishes, and all sorts of other useful things. Systemd "user" units (systemctl --user) also works here with the containers running as a non-privileged user in a non-root systemd context.

Just to be clear, Quadlet is just an integration and you can still run podman without it. You can still run podman on non-systemd systems as well.