There is no reason to think that LLMs will improve at all. They may degrade to due lack of clean training data.
If you can agree that there are certain things which can be qualitatively measured by deterministic logic (e.g. "does this build", "what is the cyclomatic complexity of this", "does this pass the unit tests", "what is the performance characteristic of this", "can this be proven to be susceptible to a XSS bug", ...), and you can see that there are ways to use this information for feedback into the models, then there's no reason to think that the available training data is finite and limited by unclean generated data.
There's several missing steps in that logic that would be difficult to (linguistically) prove with certainty, but I'm reasonably sure that your statement is false.
Your argument is that there are some reasons to agree with the statement. To show that my argument is false you actually need to show that there are no reasons to disagree with the statement. In effect you're attempting to argue that because you saw some red cars means that another person's statement that all cars are red is true.
Meta argument aside, there are many other reasons to suggest that LLMs will continue to improve, the easiest of which is they have done so recently so far.
If you read the literature from the Phi-4 team it talks about synthetic data allowing better control over the training process. The upfront investment is greater but pays off over multiple generations of trained models - and doesn’t leave you with SolidGoldMagikarp ;)
https://www.lesswrong.com/posts/aPeJE8bSo6rAFoLqg/solidgoldm...
Once humans learn enough, they are able to start coming up with and evaluating their own ideas.
This ability isn't 100% apparent with current public AI models, but I strongly suspect that this is happening behind the scenes.
Certainly researchers are already using AI extensively to improve AI, and that really has the potential to go exponential.
No amount of training data will solve this. Intelligence isn't a word prediction game.