Martin,
Very simply: no way.
Without going through the entire works, the main one that stands out is that all fuel rods on the premises, both active and "spent", will need to be cooled for many years after shutdown. Obviously, that takes energy. Lots of it. You raise an important point, one of many that remain hidden for "the greater good". Our great grand children will have to devote a huge amount of energy throughout their entire lives, and then pass the responsibility to their children, just to try and keep the 400+ active plants we have now in the world, more or less stable. Or else.