As we all know, during our higher education careers it is inevitable to be assigned essays or academic papers that require a minimum word-count. I do not agree with your premise here. For my undergraduate and graduate students I rarely include a minimum word count.
The maximum number of words you can submit for your Common App essay is 650. It must also be a minimum of 250 words. If your essays do not adhere to these guidelines, you will not be able to submit your essay online using the Common Application system. Remember that the Common App essay is designed to test your ability to write clearly and concisely, so it's in your best interest to work to.