Many times the local weather in the vicinity of the arrival/departure airport can matter not a jot, it's weather enroute, or within the TMA where departure/arrival paths are strictly controlled and separated. Aircraft which then deviate around weather add massively to controller workload, need extra coordination between different sectors and even countries and lead to a loss of capacity in the system. With airline schedules running flat out this quickly has a knock on effect to everything, lack of parking at airports due delayed outbound, lack of airport handling, crew hours, slot times, night curfews, aircraft might be out of position, airports may temporarily 'close' to normal traffic as they have nowhere to park aircraft. In fact it's absolutely incredible the system works as well as it does, for the majority of the time.