Paul is supposed to be 15 in Dune so physically, the casting was correct. His character isn't very charismatic in the book, imo, so I thought the performance was fitting. A recurring theme in the book is his reluctance to being a "messiah" and also resentment about the way he was raised/trained.
I also don't think it was made very clear in the film but the whole reason the Freman view him as their messiah is because the Bene Gesserits spread the stories/myths about a savior for (I would guess) thousands of years. It wasn't just the Freman who were told this either; they spread this message across many planets and civilizations. Paul just happened to land on Arrakis.
As someone who read the book, I thought they did a great job with what they were able to squeeze into two and a half hours. The tone and performances fit how I imagined them. The problem is there's just so much detail they had to leave out. A lot of missed subtleties and backstory that adds up to a lot when looking at the big picture.
I really, really wish this was a series instead of a movie. I strongly disagree with anyone who thinks a movie is the only way this would have worked or been greenlit. There's a lot of interesting stuff in the story but we're only getting surface level detail, if that, with the movie(s). A series with Apple's money behind it would have been phenomenal.
If they went through all the books with the different characters, ages and necessary re-casting, it could have been groundbreaking.