FAA Regs require airline Dispatcher's to track each flight's out/off/on/in times.
The definitions of those required times are used by most airlines to also consider the flight departed and arrived.

As an ex AA Operations Agent at DFW, it was my understanding that ACARS would report the "out" event when parking brake was released and all doors (cabin & cargo) were closed. From the FAA perspective, the flight has now departed, even tho the intention might be to sit on the gate awhile for traffic. One potential reason for this logic i that the aircraft is no longer on "shore power". The engine(s) and/or APU are now powering the aircraft so fuel is being burned. Dispatch needs to know when that fuel burn rate starts ... planes have returned to the gate for additional fuel after waiting in takeoff queue longer than expected !

Likewise, a flight is "in" (arrived) once the parking brakes have been set and one door is opened. At this point, the FAA is no longer concerned with tracking the flight. Pulling into the gate means the flight arrived safely, even tho there's no Gate Agent to open the door yet.

So, it's not some conspiracy to "improve the numbers". It's using the FAA definition of departed/arrived and that definition is from the perspective of "safety/flight tracking" and not "herding the passengers".