I reject the premise. I read the outputs I generate carefully (too carefully, probably). They don't "continue to output nonsense". Their success rate exceeds that of humans in some places.
To clarify: the problem I have with "statistical text generator" isn't the word "statistical". It's "text generator". It's been two years now since that stopped being a reasonable way to completely encapsulate what these systems do. The models themselves are now run iteratively, with an initial human-defined prompt cascading into series of LLM-generated interim prompts and tool calls. That process is not purely, or even primarily, one of "text generation"; it's bidirectional, and involves deep implicit searches.