Would adding anecdotes in statement of purpose be necessary? I am applying to phd programs in the US.

In preparing for the statement of purpose, I consulted some native speakers. I was suggested to add some anecdotes in my statement.

Nevertheless, after a moment's further thought, I found anecdotes occupy the space! And, I am under the impression that, since I am NOT applying to undergraduate programs nor master's programs, simply focusing on introducing my thoughts and research is the best policy.

So would a statement of purpose such that it is specific but it contains no anecdotes be considered less suitable (in whatsoever sense)?
In writing, there is a general principle of "show and don't tell" which applies.
It's not the question of to anecdote or not per se, but whether the illustration provides some insight into how you are unique.  If a (short) anecdote can illustrate something important about your creativity, initiative, or problem-solving skills, then it will help you stand out and can be useful to include.

For example, compare these two statements:


I founded a student group that teaches underprivileged high-schoolers to program.
When I was growing up, an important turning point in my education was when a friend's older brother taught me programming.  I wanted other people to have the same experience, so I organized some friends and reached out to local teachers.  Together, we founded a student group that teaches underprivileged high-schoolers to program.


The second is longer, but it tells a lot more about why what the writer did was significant and shows how they expressed initiative and motivation.