You can have a different essay for each school, but the point of the common app is for there to be one application. Creating a new version is typically done when you have new information to include on your application. A new version can only be created after you have submitted the application to a school. So, if you wanted different essays for each school, you would need to submit to the first school, create an alternate version, upload the new essay, submit to next school, etc.
The school-specific supplement is a better place to tailor you application to the school.
I think it would be a lot of work to create custom versions. Also, you are limited to 10 versions, which is lower than the number of apps you can have.