I just read this today and was previously unaware of this so-called Zeigarnik Effect. If this effect is strong, it would strike me as useful to have a record of one's completed tasks/projects, if only to protect oneself against the "remarkable fluidity" of our memory.
Most of us (me) are worried about forgetting incomplete projects, which is why we find GTD so helpful.
But it appears as if our minds are much more likely to forget completed projects. This is much more benign, which is probably why we evolved to forget them. The cost of storing them in our internal brain memory is too high. The cost of keeping hard copy files might also be too high. But the cost of keeping electronic files is becoming infinitesimally small as Moore's Law (the incessant growth of electronic memory capacity) continues to assert itself.