The American chestnut tree died out fairly early in the 20th century, long before any DDT ban. My father planted a couple of hybrids to help bring a form of them back in the 1950s.
There were still small groves and individual Elms around the country being managed through the fifties and sixties with targeted DDT spraying, and they were doing quite well. But when DDT was banned almost all of them got infected and died.
But you are correct that the large tracts of them not managed were wiped out. I was only speaking about ones they wanted to preserve, and there were still quite a few.