I got one of those Certificates of Free Circulation, from a different office of HMC & E. I had to submit proof that the aircraft was G-reg on or before some date (I forget what the date was).
The Certificate lives in the documents folder with all the other stuff, and has been produced to French "Customs/Ramp Checkers". However, they very quickly decided we weren't a problem, and whether or not they even looked at the Free Circulation I don't know.
As you say - technically not needed, but since it's free and easy to get, why not!