It seems in Big Sur the file you need to edit is not writable. So you need to make it writable first, edit it, and then change permissions back to read-only.
This doesn't seem to be strictly true - the two-line solution worked exactly as expected for me on 11.2.1. I used nano instead of vi (personal preference), but it worked nonetheless.
Maybe that's the difference. I was using vi, and not nano.
Have confirmed that using 'sudo nano /etc/pam.d/sudo' works fine.
No need for the verbosity when nano works I guess. :S