You are more or less correct about the ATC system. You have to file IFR flight plans ahead of time because it takes time for the system to process your flight

You are more or less correct about the ATC system. You have to file IFR flight plans ahead of time because it takes time for the system to process your flight plan, grant you a clearance, and assign a release time. As the ATC system becomes increasingly saturated, this process takes longer and longer. The system has to plot out every flight and schedule departure times so that you don't get too many airplanes in the same general area at any given time. Even more importantly, they have to make sure that the airports don't get inundated with too many planes at once becuase they only have so many ruways and only one plane can use a runway at a time. Commercial airports deal with that last problem by selling time slots for passenger flights, which are generally auctioned off at long intervals (e.g. anually), which is not compatible with a "leave when full" business model.