Why cut and discard the base of asparagus, before dipping in water?

For the same reason as you re-trim the last inch or so from a bunch of flowers before putting them in a vase.

The damaged cells at the original cut will have dried & sealed themselves by the time you get it home. That damage may now be extending up the next part of the stems. Cutting off another inch exposes fresh cells, still capable of drawing up water.