Sometimes, people have reasons for picking a particular door. They may be able to see inside and tell that there's fewer people in that part of the carriage, or they might intend to disembark at a station where that door's placement will confer an advantage: this is especially common in grade-separated rapid transit systems, where the placement of paths towards exits varies from station to station.
But at other times, people will try to board wherever they are able. This is likely the case if they try to board after the 'scheduled departure', which is the situation the article points to as a source of delays. And herein lies the problem: presumably, the passengers' concern about catching the train at all outweighs their desire to pick the best door. This solution is least likely to solve the situations that cause the most disruption, and is most likely to improve boarding at times when passengers have time and ability to make a discretionary choice anyway.
A low-tech strategy to try is to designate one door per carriage as an exit door, and the rest as entry doors. At a station, open the exit door first, and the volume of exiting people will curtail attempts to embark. Then after a few-second delay, open the rest of the doors and allow people to enter. This is made more effective with physical separation between embarkation doors and exit doors, such that the two streams of people don't interfere. Some newer airport people mover stations have two tracks and 3 platforms: trains discharge passengers to the outer platforms, while people wait on the center platform until the entry doors open a few seconds later. This setup is also common in amusement parks.