AI detectors simply don't work

I put a test agaisnt multiple software programs that detect AAI-generatedcontent and text. My experiment was writing multiple essays myself in a Word document and telling AI to write them again for me word for word. The results came back interesting. Some of my data showed the detectors flagging my own essays as AI but not the actual AI one; others did the opposite. I used to think that the checkers only checked for AI watermarks hidden in text, but clearly it doesn't. I told AI to rewrite an essay twice, same words and phrases. The first one came out as "Human-Written", whereas the second one came back "100% AI", which is both AI. During this study, I copied and pasted the actual AI responses straight to the detectors and the handwritten one straight to the detector This is a huge problem that needs to be fixed; students and submitters of work can get in serious trouble, especially if the reviewer relies on AI detectors. With research done, I read that these detectors work by flagging consistent artificial flow in text, which would make sense. The only problem is that it flags non-AI text as AI, or it flags AI work as human-written. Same words, same phrases, same work, different results.