i helped somebody get Doom running on an old embedded system running some 4.x kernel. we just built everything, including mesa, statically and deployed that. imagine building everything static but loading the system's libgl.so instead (which was probably just a symlink or abstraction over mesa's own implementation). what's the benefit: we'd get older, less optimized graphics routines from 5 years ago?
if you're statically linking, then just bring your own graphics "driver". the kernel interfaces are stable enough. it's not conceptually different than embedding `syscall`s directly into your application the same way you do when statically linking libc.