Absent his deferral of action, there would be no need for Hamlet to grow into his role as "scourge and minister," and no dramatic occasions at hand for his (and our) consideration of the deeper issues that Shakespeare poses in this tragedy.
A second response to this question challenges its underlying premises.
After learning of his uncle's crime, Hamlet comes into court in Act II, scene ii reading a book.
The association of Hamlet with "mere words" is strengthened by his penchant for ingenious but pointless verbal banter and highlighted by the inordinate number of soliloquies assigned to him by the playwright. (The entire section is 1,247 words.) Perhaps one of the most perplexing problems a modern audience may have with Shakespeare's Hamlet is the obvious question: what takes him so long to act on the Ghost's request for revenge?
From this simplistic (if valid) standpoint, Hamlet's delay is essential to the tragedy's narrative progression.
More important, while there is plenty of action in Hamlet (a stage work in which all of the major characters suffer untimely deaths), the play's plot is plainly subordinate to the tandem development of Hamlet's character and certain philosophical themes such as the knotty issues of mortality and chance.
Laertes tells Ophelia in no uncertain terms that her relationship with Hamlet is fruitless: Perhaps he loves you now, And no soil nor cautel doth besmirch The virtue of his will; but you must fear, His greatness being weighed, his will is not his own. He may not, as unvalued persons do, Carve for himself, for on his choice depends The safety and health of this whole state, And therefore must his choice be circumscribed Unto the voice and yielding of that body Whereof he is the head.
(1.3.14-24) The selection of a future queen is an issue at the very core of a monarchy's survival.
The pressure on Hamlet to continue the line and Claudius' desire to keep the Prince off the throne come into direct conflict.
Ophelia, as the daughter of a minister, cannot bring either wealth or security to a marriage with Hamlet.