Can I mount the root (system) filesystem as writable in Big Sur?
DISCLAIMER: have a good backup and plan to erase and reinstall your Mac from the internet before trying this procedure. A mistake can prevent your system from starting without assistance.

Disable FileVault
Reboot into recovery mode and run:
csrutil authenticated-root disable


Reboot back into MacOS
Find your root mount's device - run mount and chop off the last s, e.g. if your root is /dev/disk1s2s3, you'll mount /dev/disk1s2
Create a new directory, for example ~/mount
mkdir -p -m777 ~/mount


Run sudo mount -o nobrowse -t apfs DISK_PATH MOUNT_PATH, using the values from above
sudo mount -o nobrowse -t apfs /dev/disk1s2 ~/mount


Modify the files under the mounted directory
Run sudo bless --folder MOUNT_PATH/System/Library/CoreServices --bootefi --create-snapshot
Reboot your system, and the changes will take place