Why do you think Shakespeare gives Caesar so few lines and so little stage time, even during the scene in which he appears in Julius Caesar?
Julius Caesar simply isn't a main character in Shakespeare's Julus Caesar. Brutus is the tragic figure of the play, and the central conflict is between Brutus and Antony. Caesar is simply the focal point of the conflict between Brutus and Antony.
Actually, in fact, Caesar's assassination is the focal point, not even Caesar himself.
Also, the question of whether or not Caesar would have become a tyrant if crowned emperor must remain ambiguous, or up in the air. Shakespeare was probably limited in how much he could reveal about Caesar. The reader/viewer must not have a definite idea about Caesar's future. If Caesar is characterized as either definetely a tyrant, or definitely not a tyrant, a clear villain emerges. If he is definitely tyrant material, Brutus and the conspirators do the moral and necessary thing by assassinating him, and Antony is a clear villain. But if Caesar is definitely not tyrant material, then Brutus is clearly evil and ignoble (instead of noble) and clearly a villain.
In other words, if Caesar is thoroughly characterized the play is not a tragedy and Brutus is not a tragic figure. Caesar has to be a little realized figure for the play to work as it does.