I think NPR could compete, but I think the competitive NPR would be a different entity - more entertaining and not so insufferably snotty. For instance, the Discovery Channel started off as a commercial competitor to PBS. They’re a bit PC, but they don’t hammer you over the head with it. There’s reasonably entertaining shows like Mythbusters and such, not endless “documentaries” about how conservatives will destroy the planet.
PBS might make it but if NPR had to compete it would turn out like its identical twin (not on the) Air America.