The PhD admissions process at top CS departments is highly competitive. I think it is helpful to understand the PhD admissions process from the faculty’s perspective, and what is prioritized. It assumes a department where students are admitted by specific faculty rather than to the department as a whole. This is from my perspective based on what I see. It may not be representative and you may disagree.
Thus, the purpose of the application is to quickly convince the faculty that you will maximize their lab’s research impact as compared to other applicants.
The statement of purpose is not about your life story, or a list of what you have done, or how are generally interested in the faculty’s research area. It is to quickly provide concrete evidence that you will be the best at conducting research in the faculty’s lab under their definition of impact.
Further implications and how they apply to a PhD application is left as an exercise to the reader.