The Third Murderer may have been introduced primarily to explain something the other two murderers apparently did not know. The First Murderer says
His horses go about.
He is wondering why Banquo and his son Fleance are approaching on foot when they have been out riding all day. The Third Murderer explains:
Almost a mile; but he does usually,
So all men do, from hence to th' palace gate
Make it their walk.
This line may have been written to explain to his audience why Banquo and Fleance are walking rather than riding their horses up to the palace. It would have been impossible to bring two horses onto Shakespeare's Elizabethan stage. And even if Shakespeare considered doing such a thing, it would have been extremely difficult for the three murderers to attack the mounted riders. If three men suddenly leaped at two men on horseback, the horses might rear up and create chaos on the stage.
An alternative Shakespeare might have considered would have been to have Banquo and his son murdered somehow offstage. But the playwright wanted the audience to see Banquo being murdered so that they would be sure he was dead and had to be a ghost when he appeared at Macbeth's coronation banquet. Otherwise, some members of the audience might get the idea that Banquo had somehow survived the assault and had made it to the banquet looking bloody and disheveled. Shakespeare even has the First Murderer appear at the banquet in Act III, Scene 4, to assure Macbeth that Banquo is truly dead.
My lord, his throat is cut:
That I did for him.