For many systems the time that park brake is released is the time that is shown as the “Departure Time” and indeed under the Brake recycle this IS the time that BA are ready to push and start the flight. Delays such as local airfield, en route or de-icing slots etc are all part of the flight. Without the PBR the magnitude of such delays is far harder to quantify, without such data then it is hard for any organisation to hone in on exactly what is causing delays and make improvements. Bear in mind that any delay beyond STD is also recorded to hone in on those delays too.
My personal bug bear is that while all this effort is being made to work on departure delays, in reality this is far less important to the traveller than arrival delays - onward plans are based upon arrival time yet far less effort is put into minimising these delays. My cynical demon tells me that these are a harder thing to sort out and therefore mean they are a bit too woolly to hang bonuses on.
The other way to trigger a departure is to remote hold - push back and taxi to some remote part of the airfield and wait the delay out there. This also triggers a “departure.” How people feel about this (and indeed any) aspect of the flight process is very much a subjective thing and therefore harder to mitigate.