To some degree, Hamlet's slaying of Claudius in Act V is anti-climactic. As many critics, such as Harold Bloom, have written, Hamlet seems to have abandoned his role of revenge and slays Claudius in a kind of haphazard way that does not give the reader a great sense of revenge. Instead of being about revenge, Acts IV and V are about Hamlet's philosophical development.

For example, in Act IV, Scene 4, Hamlet finds out that a captain is going to fight for a useless piece of land. He reflects:

How all occasions do inform against me,

And spur my dull revenge! What is a man

If his chief good and market of his time

Be but to sleep and feed? A beast, no more. (IV.4.31-35)

Hamlet wonders, as he has before, about the makings of a man. While the situation should encourage Hamlet to take revenge quickly against his uncle for slaying his father, Hamlet instead takes time to consider what makes a person human. He wonders what the use of human life is if it is only used for bestial concerns such as sleeping and eating. He asks the fundamental questions about life, such as what makes us human.

Later, when Hamlet sees a gravedigger singing as the gravedigger buries Ophelia, he wonders at the gravedigger's ease with death. He says, "The hand of little employment hath the daintier sense" (V.1.61-62). In other words, the gravedigger can be casual about death because he deals with it all the time; people who don't work and who are at leisure are more concerned about death. Hamlet also marvels at the way in which the skulls and skeletons of rich people are tossed about like they mean nothing. He says:

Why, e'en so. And now my Lady Worm’s, chapless and knocked about the mazard with a sexton’s spade. Here’s fine revolution, an we had the trick to see ’t. (V.1.76-79)

He looks with wonder at the reversal of fortune the wealthy woman has suffered after she has been reduced by death to a heap of broken bones. Hamlet's reflections about the uselessness of life and casual quality of death soften our perception of his murder of other characters in the play.

In Acts IV and V, Hamlet develops his philosophy about life and death—about what death means and how it defines us. His slaying of Claudius is predictable, and it is not the main feature of the play. Instead, the play is about Hamlet's development, and without the last two acts, Hamlet's philosophy of life would be far less developed. 

A good solid question. First, he would have avoided killing Polonius. This would prevent him understanding as fully that violence spills over.

Second, the nature of the scene with his mother would have been radically different. Less angry, more defensive.

Third, he and we would be less exposed to reflections on death (the hidden body, the Yorick in the graveyard scene).

Fourth, he would fret at his old friends less (Rosencrantz and Guildenstern)

Fifth, Ophelia would not be dead, he would not feel responsible, and he would not be aching with the realization of how badly the world is going.

Sixth, the final scene of mass betrayal and the darkening world picture that comes with it would have been avoided.