In most cases, the u (undo) command will be useless after text-input mode because the arrow keymap does several hidden commands -- and u can only undo the single previous command. The only "undo" command that will do much good is U -- it undoes all changes on the current line, and it probably won't work if you've moved off the line since you made the change you want to undo.
Beginners can get confused by this. They need to learn that vi is a moded editor -- that you enter text in text-input mode and make changes in command mode. Movement through the file is with commands.
When people start using vi and they find that some motion commands (the cursor keys) work in text-input mode, vi seems inconsistent.
If your map! runs commands that start with an ESC (and it almost always will), your ESC key may work more slowly. That's because every time you press the ESC key, vi will wait one second (or so) to be sure that the ESC is just an ESC alone and not the beginning of a map! sequence. Some versions have changed this, though.
The fast alternative is to press ESC twice. That rings the terminal bell, though.
-- JP
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