According to Wikipedia, a codicil is as follows:
In the United States, a codicil is a document that changes an existing will. Amendments made by a codicil may alter, explain, add to, subtract from, or confirm – and otherwise amend a will in any other way, minor or major, short of complete revocation. It is subject to the same formal requirements as a will.
I would think that it would be just as easy to print off a new copy of the will with the necessary amendments, so time saving wouldn't be a reason to create a codicil. If it has the same formal requirements as a will (which I take to mean it needs to be signed by witnesses and such), then why would a person create a codicil?