The alternative is to "turn in a good paper" which is not quantifiable and thus anathema to the modern Taylorism inspired world of education. If the student can't agree, it's a problem and so word count it is - can't argue with basic math.

There are still unquantifiable aspects of grading. Just turning in 1000 words or whatever doesn't guarantee an A, it's a bare minimum in a still-mostly-unquantifiable grading system.