You'll still be able to test writing, but going forward it will need to be done in a proctored setting. Similar how you would test grade school math given the existence of calculators.
You need both memorization and applied reasoning to be taught in school. Without something to apply reasoning to you can’t really reason about anything. And without applied reasoning, memorization is pretty useless.
If the ai can get a good answer, the questions must be fairly well constructed, and it's reasonable to expect a student exposed to the same info could also come up with a good answer.