re: Christmas boxes for the Men

Passing the cord through would interfere with the smooth removal and replacement of the trays.  Same if a knot inside the box for cord ends.  Even  If the cord was passed through there would still be two cord ends to deal with on each handle.   
I was a bit concerned on the way the cords were fastened in the article.  Testing their method I found it quite simple to do and very secure.  

Those tight dove tails are actually box joints.   Done with Incra jig on the router table.   My usual way to make box joints. 

Thanks for the comments.