As a pilot and a FISO I believe that the reason that pilots ask for flight plans to be "closed" is that they do not understand the process.
Within the UK the destination airfield will initiate overdue action* if an aircraft fails to arrive within 30 minutes of its ETA. Therefore what is the point of the destination airfield sending an ARRival message ("closing" the flight plan) since all that the ARR message does is inform the destination airfield that the aircraft has landed?
The one time that an ARR message will be sent is if the aircraft diverts in which case the airfield at which it has landed will send an ARR message so that the destination airfield is aware that the aircraft has landed safely.
* There are other times when an ATSU will initiate overdue action but these apply irrespective of whether or not a flight plan has been filed.