popular culture is much more fractured now into lots of small scenes
That's definitely a big part of it. But popular culture is also set up differently now where a different kind of person breaks through. There are some really great songwriters out there with Dylan-esque bodies of work (John Darnielle, Adrianne Lenker, Josh Ritter, Kristian Matsson are a few one might argue for). But the modern system isn't set up to create new Dylans.
A big part of Dylan's personality is his reclusiveness and mystery. He spun his own story, made up details, and generally just didn't reveal much of his true self in the press, but meanwhile the press constantly talked about him. But in the modern music industry, performers are asked to build an authentic social media presence before they can even get a record deal. If they want to go solo, they have to essentially build a direct marketing company. There's not much space for someone to be a mysterious recluse. It's part of the reason we have very, very few new "movie stars" in the classic sense of larger-than-life personalities.