Earlier quoted context omitted.
Your use case makes sense, but 1) Git's current initial setup UI would not prevent the user from making that mistake. It might make them feel stupid when they remember, but that's not the same thing as usability. The commit interface displays your identity and might throw up a red light. 2) Having made this mistake, a new user isn't going to remember the "git config" or "git commit --amend" commands they copied when…
In the common case, a lack of username/email actually indicates a configuration error. Blindly offering to set username/email may cause people to "fix" their config by re-setting username/email when in fact the lack of this is indicative of some other issue. Sure, _everybody_ sets up git once, but on the other hand, everybody sets up git _once_. The common use case is, by far, running with git already configured.
1. You edited it by hand and fucked up the syntax. In this case git could print an error instead if offering to add the username/email.
2. You deleted itself. When git asks you for the username/email again it'll actually tell you that that file was for storing the username/email.
3. Filesystem error. A faulty gitconfig with be the last thing the user is worrying about.
All in all I don't see how all of this would imply that prompting a username/email isn't a good idea.