If you are applying to several different schools using one generic statement will be easily recognized and just as easily dismissed. WHY _ because you will be seen as not making an effort sell yourself to this particular school, low effort equals low interest to admissions representatives. Remember the admission committee will likely view thousands of these statements from qualified candidates and they will spot a weakness, flaw or lack of attention to the process in a heartbeat. What you don't want to do is give this committee an easy excuse to dismiss your statement and application.
Often, the first draft is not the essay you originally envisioned. You might even discover that your ideas about your theme have changed as you have been writing. If you do not like the way certain sections are stated, re_arrange them. Once you are pleased with the body, make sure the conclusion and introduction still match it and complement the way you see your topic at this point. If not, rewrite them to fit the essay you did write and the way you see your topic now.