I suspect the production version will have a covering on the sidewall for that and to reduce aerodynamic drag. It won’t be structural like current tires but I think the “wall-free” design you see now is Just prototype marketing.
This was researched and practiced since at least first world war, with pioneering applications dating to 1850s.
TLDR: internal friction in the rubber kills it. Acceptable for military and heavy-duty vehicles, useless for anything else.
It doesn't matter. So long as elasticity is provided not by gas compression, but solid material compression/tension, that solid material will deteriorate fast.
Downvote me all you want, but this idea won't fly. It can't compete with regular tires at anything above 20mph.