There are plenty good reasons not to.
1) You never know how it is going to be taken by the admissions office. Sure, you could think it sounds like you are ambitious and want to help, but it comes off more as pompus and that you want to have control over others. It is a very unrealistic view of how it works, especially in the public interest sector. Sure, eventually you may be able to be in a position where you are calling the shots and shaping policy, but right out of school you are likely going to be working discovery and going through documents, not actually stepping foot in a courtroom or boardroom directly affecting policy.
2) If that is the only reason you want to be a lawyer, you will find it tough. Sure, it may sound sexy to change the world, but the facts are, its the small battles that do it, not the big media circus ones. It takes a lot to fight day to day, and the fact that the reason you want to do it is power, doesn't come off that you have done your research.
3) A lot of people change what they want to do in law school, so it is not always the best thing to say "this is exactly why I want to come" unless it plays into a stregnth of the school itself, where you can show actualy statistical research about the school you want to attend.
For a little more hints I found this for you http://www.top-law-schools.com/statement.html
, but again, if you haven't sent out that statement yet, I wouldn't. It might be very well written, but remember, you do not know who is going to read it, and think of the different ways it can be percieved. Saying "I want power" can be viewed as a HUGE negitive. When schools accept 20-40% of all applicants, you don't want to give yourself any room to screw it up.
Good luck on it though! I am not an expert in this, so I could be wrong, but its just my two cents.