Why memorize a different command? I assume sudoedit just looks up the system’s EDITOR environment variable and uses that. Is there any other benefit?
I don't use it, but, sudoedit is a little more complicated than that.
details
from man sudo:
When invoked as sudoedit, the -e option (described below), is implied.
-e, --edit
Edit one or more files instead of running a command. In lieu
of a path name, the string "sudoedit" is used when consulting
the security policy. If the user is authorized by the policy,
the following steps are taken:
1. Temporary copies are made of the files to be edited with
the owner set to the invoking user.
2. The editor specified by the policy is run to edit the tem‐
porary files. The sudoers policy uses the SUDO_EDITOR,
VISUAL and EDITOR environment variables (in that order).
If none of SUDO_EDITOR, VISUAL or EDITOR are set, the
first program listed in the editor sudoers(5) option is
used.
3. If they have been modified, the temporary files are copied
back to their original location and the temporary versions
are removed.
To help prevent the editing of unauthorized files, the follow‐
ing restrictions are enforced unless explicitly allowed by the
security policy:
• Symbolic links may not be edited (version 1.8.15 and
higher).
• Symbolic links along the path to be edited are not followed
when the parent directory is writable by the invoking user
unless that user is root (version 1.8.16 and higher).
• Files located in a directory that is writable by the invok‐
ing user may not be edited unless that user is root (ver‐
sion 1.8.16 and higher).
Users are never allowed to edit device special files.
If the specified file does not exist, it will be created. Un‐
like most commands run by sudo, the editor is run with the in‐
voking user's environment unmodified. If the temporary file
becomes empty after editing, the user will be prompted before
it is installed. If, for some reason, sudo is unable to update
a file with its edited version, the user will receive a warning
and the edited copy will remain in a temporary file.
tldr: it makes a copy of the file-to-be-edited in a temp directory, owned by you, and then runs your $EDITOR as your normal user (so, with your normal editor config)
note that sudo also includes a similar command which is specifically for editing /etc/sudoers, called visudo 🤪