Shakespeare himself must have realized that Brutus was a more sympathetic character, but he wanted his play to be titled Julius Caesar because l Caesar was one of the most famous figures in world history, whereas Brutus did not distinguish himself as much and was remembered mainly as one of Caesar's assassins.
Shakespeare had his reasons for not writing a play which would end with the death of Caesar. For one thing, the aftermath of the assassination was of great dramatic interest, especially the way Antony turned the mob against the conspirators and then defeated them at Philippi.
Shakespeare must have been fascinated and inspired by the challenge to write his version of Antony's funeral oration in his own English iambic pentameter. The speech is one of Shakespeare's greatest achievements, possibly the best thing he ever wrote. It not only turns the Roman mob around, but it turns Shakespeare's audience around. They have been identifying with Brutus and Cassius up to this point in the play; now they are identifying with Antony and Octavius--as well as with the vengeful spirit of the mighty Julius Caesar.
Shakespeare tries very hard to maintain the impression that Julius Caesar is still a dominant presence even after his death. Antony sets the tone in a marvelous soliloquy in Act 3, Scene 1.
O, pardon me, thou bleeding piece of earth,
That I am meek and gentle with these butchers!
Thou art the ruins of the noblest man
That ever lived in the tide of times.
Woe to the hand that shed this costly blood!
Over thy wounds now do I prophesy,--
Which, like dumb mouths, do ope their ruby lips,
To beg the voice and utterance of my tongue--
A curse shall light upon the limbs of men;
Domestic fury and fierce civil strife
Shall cumber all the parts of Italy;
Blood and destruction shall be so in use
And dreadful objects so familiar
That mothers shall but smile when they behold
Their infants quarter'd with the hands of war;
All pity choked with custom of fell deeds:
And Caesar's spirit, ranging for revenge,
With Ate by his side come hot from hell,
Shall in these confines with a monarch's voice
Cry 'Havoc,' and let slip the dogs of war;
That this foul deed shall smell above the earth
With carrion men, groaning for burial.
Antony says Caesar's spirit will be responsible for all the death and destruction that will follow. Then Antony uses Caesar himself to inflame the Roman mob. Antony reminds them of Caesar's victories, of his concern for the people, shows them his bloody mantle, then his mutilated corpse, and finally reads Caesar's will.
Before the Battle of Philippi, Brutus is visited in his tent by Caesar's ghost. Brutus later says that Caesar has appeared to him on two different occasions. This is apparently intended to remind the audience that Caesar is still present in spirit and that everything is happening because he is directing it, just as Antony predicted.
When Cassius and Brutus kill themselves to avoid being captured, both men acknowledge in the last scenes of the play that they have been vanquished by Julius Caesar.
CASSIUSCaesar, thou art revenged,
Even with the sword that kill'd thee.
O Julius Caesar, thou art mighty yet!
Thy spirit walks abroad and turns our swords
In our own proper entrails.
Runs on his sword
Caesar, now be still:
I kill'd not thee with half so good a will.
Well, Even though Caesar is killed in the third act itself, Caesar is still the main character and not Brutus. Just because Brutus doesn't die, doesn't mean he's the protagonist. The whole cause of whatever happend in the 4 and 5 Act is because of Caesar and Caesar's spirit lives on throughout the play. Brutus just talks about Caesar. Whatever Brutus does is aall come down from the death of the protagonist, Caesar.