According to ICAO documentation the FPL is valid +30 minutes (no minus value).
"In the event of a delay of 30 minutes in excess of the estimated off blocks time (for a controlled flight) the flight plan should be amended or a new flight plan submitted".
As has been aluded to by previous posters, a flight departing earlier will not have been checked for restrictions along the filed route. Not just ATC/Flow restrictions, but route closures, military activity, etc.
There are also ATC systems to consider, often the data on early flights will not be displayed in front of the controller. There are others better qualified to fill in the numbers applying in this instance but this might explain the -15 minutes parameter.
As has also been stated, a call to the tower controller can (at his/her discretion) result in a Ready (REA) message being sent which can bring forward the EOBT by up to 30 minutes.
DFC you say: "Unfortunately, the flight plan system has not quite kept up with the times. It should be possible to submit a change message to bring forward an EOBT. "
This used to be possible. It was stopped because some operators were using this facility as a means to "cheat" the system by repeatedly updating EOBTs backwards until the slot matched the required departure time.
flowman