Depends on the size of the terminal too! How long will it take you to get from check-in to the gate? You can't guarantee that you will go straight to the plane. Time and time again you tell the pax to go straight to the gate, and they go duty free shopping thinking they have enough time still. The bags are checked in, but the main bulk of the bags have gone to the aircraft, therefore so too have the baggage handlers, and your bags are still sitting in the baggage bins under neath check-in. Also, the weights and fuel have to be worked out for the flight deck to program into their computers. They won't know this until check-in has closed.
If the aircraft has an air traffic departure slot, ( which in most cases they do), the airline has around 10 mins to close doors and become airbourne. If you are not airbourne in this time, you miss the slot and you may have to wait a long time for another one to become available.
Aircraft are not taxi's so you can not call them back or hold them back. They have to stick to strict time schedules and it is vital that they make them. There is a lot of work that goes on behind the scenes before an aircraft can depart, therefore the need for the check-in to close on time is critical.
The paper work for weights, and loading is not done at the aircraft, but in the ground handlers offices, which could be 10 mins away from the aircraft. So 30 mins is not a lot of time to apply any changes to the Passenger loads or baggage.
Don't forget that once the check-in closes the staff have moved on to check in another flight. They have not finished their work. So there are also staff problems. Also once the baggage handlers have loaded the bags, they too move on to another aircraft.