If the goal is just preventing full root privileges, a CapabilityBoundingSet in a systemd unit will do.
However copy fail can be used in many other ways not contained by containers or the above settings. For example it can modify the /etc/ssl/certs to prepare for MitM attacks. If you have multiple containers based on the same image then one compromised CA set affects another.
I added these
to my .service. Is it good enough?