The only purpose I can see is safety. Depending on the size of the cage you could develop a significant charge and "possible" shock hazard. That being said, all items stored inside the cage need to be electrically isolated from the internal surface. This is in regards to electronics protection and not radio work.
My personal opinion is that many devices will not be effected by EMP. YMMV, but battery operated devices without antenna should be just fine. Anything not plugged in should mitigate many of the problems of long line issues.
My greatest concern is still the installed inverters in a backup system. Further, imagine the wiring in the walls of your house. This is one heck of an antenna.
For more information check out this
Wiki Link (it is wiki, but pretty decent). Pay particular attention to the discussion on E1. This is the electronics killer, but requires a high degree of sophistication in weapons construction. There is a discussion here where concerns are raised that E1 will damage protective devices that would protect against the second E2 (think lightening and static electricity) component. That I don't know about. Finally there is a discussion of E3. E3 is not static electricity. E3 is the component equivalent to the effects of CMEs.
One of the issues barely touched on is the penetrations and jonts in a building or space to be protected. Doors, windows, eaves, wiring penetrations, ductwork, pipe, fire protection, sanitary sewer, storm drainage and downspouts, hinges at door frames, knobs and other thru-wall details, and a host of other items play a part in allowing RF into areas to be protected from this issue.
The only purpose I can see is safety. Depending on the size of the cage you could develop a significant charge and "possible" shock hazard. That being said, all items stored inside the cage need to be electrically isolated from the internal surface. This is in regards to electronics protection and not radio work.Thanks for your detailed reply, the link, and for adding what I forgot to put in. You're absolutely right about electrical isolation for items inside the cage.