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.