To Rewire or Not To Rewire....  

Rewire
Go for rewiring, it is a lamp worthy of the attention, depending on what part of the world you are in rewiring maybe essential due to rules and regulations so anyone interested will probably rewire. If you are worried keep the old wiring.

Thank you
It's one of those things... My daughter likes it, but then she is also 14 and most likely won't like it next week...wink...so.... If it is worth more to someone else as is, I'd rather sell it, let them fool around with the electrical aspect and let my daughter pick something already wired and new - say an IKEA "disposable".... lol.

It doesn't
have antique cloth wire, but modern plastic lamp cord -- to which you can easily apply a hardware-store clamp-on plug without tools. Either way, you haven't ruined the piece.
We don't see the present plug, so no way to know if it's worn out. You can cut it off, leaving a clean end to attach a new one.
Is it missing a thumb-screw or wing-nut at the central hub ? How is the clamp loosened and tightened for adjustment of the arm ?
Nice-looking light !

Reviving
an old plug is often as simple as straightening the prongs with pliers. The sort of plug with prongs made of folded brass -- so each prong is a two-ply affair -- are especially designed to be kept in service; a knife can be inserted between the plies of the prong, and with a little twist the prong can be "fattened" to engage better with the outlet or extension cord it is mated with.
Easy as pie. A case where a bit of technology goes unrecognized and ignored ?

cloth covered wire on top
Hi there -
It has cloth covered wire from from the handle piece to the actual lightbulb screwyiny thingie and that's where it's wiggling loose and wires are starting to expose. Plastic cord is not terribly pliable either and I wonder if that is a function of the cord aging or just the type of sheathing that was used for it.
I'm not afraid to rewire so much as just wanted to make sure that if it were worth more than an IKEAish lamp to someone, I'd rather leave it to them and let Miss Thang get something brand new. 😉
Thank you all so much for your kindnesses and help!