I have faced a similar issue in the past, and I don't understand how static binaries from the host are supposed to solve this.
From what I remember, GPU access on Linux 'works' by accessing specific FDs under /dev, which are vendor specific - this is what these libs do under the hood.
The libraries don't have any magic powers - if the FD is inaccessible, you won't be able to do anything.
So there's some vendor specific access needed in containers anyway (or a blanket allow, which is a BAD idea).
Also not sure why dynamic linking isn't good enough for this - the issue lies with the permissions, not how you load/link libraries.