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.
This is obviously stressful, and psychologically pressures you to try to finish the task ASAP the day before, so that you can come up to the meeting and just say its done.
Which is the real actual benefit of the standup, and why managers keep doing it, despite they are obviously not needed and in most cases a waste of time.
The standup keeps everyone on their heels and feeling like their every breath is monitored and accounted for.