The national media has already come out pretty strongly with the "What's wrong at Carolina?" stories. If we miss the NCAAT again and we move on from Hubert, I don't think you'll see a huge backlash as most of the national media will fully understand why our results over the last 4 years fall short of the standard at a school like Carolina. I wouldn't be surprised to see a small amount of clickbait articles that might take a negative view, but I would expect those to be a distinct minority of stories.
If it happens, and assuming we go outside the family for a new coach, I think you'll see it much more often used as a jumping off point for a lot of "Look how much college basketball has changed!" stories. The easy story is that college basketball has changed so much that even staid ol' "keep it in the family" Carolina has had to make major changes. And while that's not an incorrect take, it'll miss that the biggest issue we face isn't "the changing world of college basketball", it's that we made a very shortsighted hire 4 years ago and we've paid a significant price for it since.
In terms of the coaching fraternity, I don't think you'll see the backlash you're expecting either. And that's not because they don't like Hubert (I assume they do), but a lot of them are going to see it as he didn't pay his dues before getting the head job at Carolina and that's a lot of what led to him being in over his head in the role. Many of them very much remember what it's like to start as an assistant at a smaller program and then work their way up the ladder as an assistant at progressively bigger schools before returning to a smaller school as a head coach to try to climb the ladder back up as a head coach. Alternately, Hubert was recruited by Roy to start his coaching career as an assistant at Carolina and then chosen directly by Roy to be the HC without a real search. I would imagine that a number of coaches aren't going to have a great deal of sympathy for Hubert given that path to the job, especially since most of them won't really sniff jobs as prestigious as "Head Basketball Coach at the University of North Carolina". There were discussions about how Roy, even near the end of his career with all his success, was at times viewed by other coaches as a "golden boy" who hadn't paid his dues and had only done it at blue blood programs. And if other coaches are going to feel that way about someone as successful as Roy, they're not going to have any more sympathy for Hubert who has had so much less success at a blue blood program.