If the only case is git... which by the way behaves in that way even
on Windows... isn't it a git problem?
I like not having a default editor and a more user-friendly approach
would be to ask the user what they want on the installation or on the
first run.

git is not the only program that uses the EDITOR variable. Some configuration tools on the command-line, such as crontab, will use the editor set in the environment variable if there is one.

-Ian