Its the perception of yourself and your work from the eyes of the group that is at stake here, it's important and most people usually don't just improvise it.
Many times people have notes of what they want to say, which involves preparation, attention and energy put into it that would better be directed elsewhere.
It requires very little thought.
I've prepared for standup when I was new to a team, but it should pretty quickly get to the point where you don't need that. At least for my experiences, it's not like standup is a major factor in how teammates think of you - that comes from working together with people.
If your teams have so little trust in each other that you have to do all this preparation for a standup, then there are already much larger issues.