Yeah, but disk ids are not uuids.

/dev/disk/by-id seems to be a good way to find those disk ids in order to pass
them to grub-install.  I doubt that this can be made OS-independent--even the
udev rules specify different variables for different devices, sometimes it's
bus id and serial number, sometimes it's name and serial number, sometimes it's
ieee1394_id, sometimes ID_WWN_WITH_EXTENSION.

Alternatively, grub also works from a boot-active partition--it nothing else
works, we can install grub to a partition (for example the root partition).

Then, migration would be difficult, though (if people had grub installed on
the MBR, that destroyed the previous loader that would have loaded from the
boot sector of the partition).