And that's exactly the point! By making sure the student can't edit the entire text once its written, you force him to think about the essay's structure and force him to plan much more before writing :)
Sure, but you know that professionals edit, right? It improves the quality of the product.
If the goal is to assess the ability of the student to produce a professional product, then why prevent them from using AI in the first place? The vast majority of professionals have access to AI nowadays?
Most curricula should probably feature both forms of assessment, demonstrating your knowledge of the basics in a closed book assessment and your ability to produce high quality final products using all resources available to you in take home assignments.