Why do I not have sufficient permission when running sudo as a user

sudo -u chris runs the given command as user chris, not as root with USER set to chris. So if chris can’t access /root, sudo -u chris won’t change that.

See man sudo:

-u user, --user=user

Run the command as a user other than the default target user (usually root).

sudo isn’t specifically a “run as root” tool; it’s a “run as some other user or group” tool.