While I agree a modern glass covering would be nice, don't underestimate the improvement from new paint and cleaned up / replaced lighting underneath (or just making sure light bulbs work and are replaced when they burn out

).
It will make a big difference. I thought I noticed they were painting the other day so hope the other report here is confirmation that they really are.
At the risk of making too many comparisons

, when I first moved to DC they were recovering from many years of financial neglect. One of the things that had been "skipped over for lack of funds" was taking care of the grand circles where one of the roadways actually passed under the circle through tunnels. The railings, benches, and lighting around the park and along the streches between the varying road levels looked crappy - lights burned out or just gone, paint peeling, weeds growing wherever they could get a foothold, benches missing or broken. Even when the streets and sidewalks leading up to them were nice, the circles were depressing instead of expansive and uplifting.
As the city finances recovered, they started work on the circles one by one. When they began the work on the one nearest my condo - one of the first they tackled - I was SO disappointed that they didn't change anything. They just cleaned up what was there, replaced / repaired the lights and benches, got rid of the weeds, and then started scaping and repainting the railings the SAME dull green colour.
But when it was done, it was fine - more than fine. It managed to still look historic, and the older colour actually fit because it was understated and didn't attract attention to itself. What you noticed instead was the circle and the details on the lighting, etc. That colour and style had clearly been chosen so it would have a presence yet be subtle.
So I think painting the HBC awning and just cleaning it up so it doesn't detract anymore would be fine. It is one of the better awnings to walk under. Even in disrepair, it doesn't leak like some of the new modern ones do. It doesn't have little gaps. I think the main issue is it's ugly and draws attention to itself now. If it were clean and painted and the lights worked, I wouldn't even think about it (which is what's intended). It doesn't have to be some "tricked out" display in itself. It just needs to look nice and "disappear" as a presence in itself

.