Damn, from worshipped to wiped out in a human lifetime. That's a shame.
As far as why they're not listed as extinct yet, it's really hard to definitively say there are none left. It's a big river and while surveys haven't turned any up in a long while, it's possible there are individuals out there still. One of the species I sampled for hasn't been seen in the state's waterways for decades. The last stream it was seen in was ruined by the landowner and is no longer suitable habitat for the species. There's other streams with suitable habitat, however. If the species exists there and is prematurely declared extinct, the legal protections on those streams are gone and those fish will be gone within a few years for sure.
It's also kind of political. Maybe that fish is gone, but those streams harbor other species which need protection, but have not been listed as endangered yet. Species don't automatically get listed as protected. Someone has to care enough to gather the data and advocate for protection and listing as threatened or endangered. This can take years or decades and a lot of funding. One species listed in a disappearing habitat may also protect a half dozen or more bug species, plants, crustaceans, etc, which do not have the extensive data available or anyone focused on getting them protected.
Oh, and then someone also has to care enough to sue the entities that aren't going to abide by the Endangered Species Act until they get sued a couple times. I'm not exaggerating. My first reality check as far as how conservation really works was an internship surveying a very cute and popular (among bird people) species of bird. The woman I was working for spent a decent amount of her time taking businesses, land owners, and other sectors of the government to court for flagrant violations of the laws protecting the species.
And funding, don't forget funding. Those grants for the protection of that species are gone the second it's declared extinct and the biologists who rely on that funding to maintain species inventories in those areas can no longer afford to hire techs to slog through the middle of nowhere and inventory extant species.
Generally, the only people in a hurry to declare a species extinct are those who want the protections lifted on that habitat. Maybe it's a little dishonest to take so long declaring a species extinct. Honestly, even if there are 10 Yangtze paddlefish left out there, the species still isn't coming back. However, as far as environmental health is concerned, it is beneficial to drag that funding and protection out for as long as possible, even when the listed species is well beyond saving.