Wouldn’t it be possible to make Anti aliasing or depth of field using the persistence of vision? It would require only to move slightly the camera so that the eye sees the view from several positions in same time. Tell me if it’s stupid 
and tell me if it’s not.
No, it’s not stupid. In fact, I have been investigating on this for some time now. Doing some temporal antialiasing isn’t that bad, and using the same means for improving texture quality can be quite useful.
In fact there’s a problem if we don’t use vertical synchronization and so we’re limited by the screen frequency.
This Siggraph '94 paper on frameless rendering may interest you:
http://www.cs.unc.edu/~scher/fr.html