As per the common view above, VFR FPLs are of limited use unless filed for legal reasons e.g. international trips.
The most useful a VFR FPL can be is for traffic volume planning at ATC controlled airports. More FPLs mean more staff need to available to cope with the capacity at the correct time. For en-route agencies it's more paperwork to read for the sake of a quick RT exchange.
Also FPLs do provide a 'tracking' tool should an emergency occur e.g. SAR. Or perhaps the destination needs to find out who is controlling a planned inbound flight to advise of poor weather or airport unavailability i.e. something else crashed into the runway and its no longer fit for use. A way of providing an early warning to divert if you will. These rely on a flightplan being activated via the departure message (DEP).
As for overdue action (OA), it's usually the responsibility of the destination airport to take OA when:
1. a fixed wing aircraft fails to arrive at or is not in contact with the destination aerodrome at the earliest of i) ETA radar entry or other specified terminal calling point, or ii) ETA overhead or landing.
2. a helicopter fails to arrive at or is not in contact with its destination i) at the end of its notified endurance for flights over water, or ii) one hour after the end of its notified endurance for flights over land.
These of course the latest times that OA should be taken, and do not prohibit OA being sought if doubt exists as to the safety of an aircraft. But departure aerodromes are not normally responsible for OA. Emergency action is of course taken by whoever is nearest.
At a controlled airport a FPL will be closed on arrival by ATC/flight planning/airport operations. For uncontrolled aerodromes it is the captains responsibility or sometimes even an AFPEX fluent radio operator.
For aerodromes without ATC such as Radio or Information stations... this is all more or less irrelevant. I stick to the CAA guidelines ref. VFR FPLs: no submitted unless I have to or flying over inhospitable terrain... neither done very often
