Like it says in the man page, git add -p "effectively runs add --interactive, but bypasses the initial command menu and directly jumps to the patch subcommand". Interactive mode does support adding untracked files.

Not what I'm asking. "add -p" will offer deletions, but it should also offer to add untracked files, essentially showing a diff with all lines added (with an empty file as the base).

"add -p --all some_untracked_file" does nothing, "--interactive" does something completely different; a menu system, not a "yes/no/etc." patch prompt.