Wrestling is not just a sport but a life skill. If you can perform and defend a double leg takedown you have a huge advantage over your average street fighter, because transitioning to a choke that ends the tussle is then pretty straightforward. Then there are the cases where brawlers are basically hugging each other, in which case knowing throws and trips makes this a mismatch: wrestling is skill, you can learn moves that give one a large tactical advantage. Having the confidence from knowing you can physically defend yourself is extremely valuable even if never used.
Further, unlike team sports, in wrestling you have to master the issue of hating to lose but not being fearing it. Young kids cry a lot when they lose in wrestling compared to soccer or baseball. Unlike in team sports, losing is a direct assault on their ego, not merely because it's one-on-one but because the humiliation is not nuanced: some guy just pushed you around like a rag doll. Learning how to cope with unambiguous defeat is an extremely useful life skill that kids today are often sheltered from.
Yet, as wrestling declines, mixed martial arts like the UFC rises, so the future is not horrible for the gist of my favorite sport. Further, I never really understood the greco-roman wrestling rules as applied in Olympic matches. Human combat will always be interesting to humans, and any competitive combat will have some peculiar rules like in wrestling, judo, or boxing, and those sports with the better rules will thrive, though perhaps not in the Olympics.