Sure, that is true right now. But in not-so-distant future

Today it is a statistical model

Tomorrow it is a statistical model

Check out the OpenAI peer review article on "AI Scaling Laws", although it had its math corrected by the staff of DeepMind later on it still more or less correctly predicted the performance of every model since and predicts that we're hitting a hard limit soon as training approaches infinite but returns become smaller and smaller. If you plot the performance as per their charts then the limit after INFINITE training with INFINITE sample data and INFINITE power used then you get about 94% accuracy, which is still less than any one singular human's capabilities. So why train it when you can just go and get a random human?

Clearly this approach doesn't work.

You mentioned a theoretical model which adjusts its own weights? We call that self-sampling which leads to feedback loops and model collapse.