Clever solution, but I agree with the others. I have fair skin & a very long commute by any standards outside of LA, DC or Chicago (50-60 minutes one way during non-rush hour with good weather, up to 2.5 hours one way if there is bad weather & accidents), so I was getting way too much sun on my left arm. My solution? Apply sunscreen with zinc oxide in it to my left arm (and, of course, my face). I need the sunscreen for my face anyways & it doesn't take that much more to apply some on my arm during warm months when I'm wearing short sleeves.
The two primary issues that would keep me from buying your sleeve are: (1) there is no protection for the hand, so I would end up with a glove-like sunburn on my left hand, and (2) I would worry about whether it might be uncomfortable to be moving my arm around with that loop around my neck. The second one may be an unfounded worry, but it was the first thing that came to mind. I suppose since it's not actually holding the arm up, that wouldn't be a problem (maybe?), but visually it reminds me of a sling and I remember how uncomfortable that was for my neck.
I do agree that if you find a market somewhere for this item, it needs to be made in a non-quilted material & without applique to keep it as lightweight as possible, and in a light color to reflect away as much heat as possible.