The opening of the cave sure lends itself to a couple of concrete trucks backing up and filling it.
I don't think shutting it down is a good idea. Sounds like this cave kept the search and rescue team pretty busy. OTOH there were thousands of visitors every year. A compromise would have been to seal the dangerous areas, including the one with the body, but keep the easier stuff open and continue to control access. Now the adventure seekers will go elsewhere and keep some other S&R team busy ...
George