In Shazam! (2019), the oldest wizard apparently has the powers of Solomon, Hercules, Atlas, Zeus, Achilles, and Mercury. Despite having these, why does he die? On similar lines, another question is "Can Shazam die?"
On the comics, he is Immortal. In the movie, he is not.
My job is to protect you the seven worlds of the seven main sins. But with time I'm getting weaker. Therefore, I'm looking for a champion to whom I can give my strength.
Since he is growing old and weak, he transfers his powers. As soon as he is powerless, his body crumbles due to his immense age. Because Billy seems to have the same powers, I think we can theorize that he will also age (although he may live an incredibly long time, similar to Super-Man).