Well generally yes, it is the quickest and most succesfull method. Having it written down seems to leave a lasting impression in your brain. When you give yourself the opportunity to try having to remember it your brain can come up with all kinds of excuses not to, but hen you force yourself to write it down, you do it and it's there forever.
To me it's more about identifying emotions and moments of awareness in the dream, the actual content does not have to be elaborated on as long as you go over what went wrong and where you should have turned lucid.