Does not the fuel, inside the wreckage of the reactor building, continually produce new I-131, Cs-134, Cs-137, Sr-90, Radon, Xenon, and a host of others? The fuel is no longer critical, but fission of the enriched Uranium is ongoing. That's why the stuff is still physically and radiologically hot. Production of radionuclides will be ongoing for many thousands of years.
It's true that the nuclides will be more or less contained inside the reactor building, but some of it will seep out, because it's not hermetically sealed like the reactor containment was. If you seal it (ie. make an airtight sarcophagus) - then heat from decay will build-up. It requires air circulation to cool, and that's the whole point of the sarcophagus. It will still allow some byproducts to get out, and will affect all of those who are nearby; and this will continue until the fuel cools enough for workers to get in there, physically remove it, and put it into sealed storage.
It's the ongoing release and exposure of these materials that is the health-hazard. And it will remain so for thousands of years. This is precisely why safety systems for nuclear plants are so highly engineered. This was the scenario they never wanted to happen.