Consider that even the named phenomenon is sloppy: "recursive self improvement" does not imply "self improvement without bounds". This is the "what if you hit diminishing returns and never get past it" claim. Absolutely no justification for the jump, ever, among AI boosters.
> If AI ever gets to human-level intelligence
This picture of intelligence as a numerical scale that you just go up or down, with ants at the bottom and humans/AI at the top, is very very shaky. AI is vulnerable to this problem, because we do not have a definition of intelligence. We can attempt to match up capabilities LLMs seem to have with capabilities humans have, and if the capability is well-defined we may even be able to reason about how stable it is relative to how LLMs work.
For "reasoning" we categorically do not have this. There is not even any evidence that LLMs will continue increasing as techniques improve, except in the tautological sense that if LLMs don't appear to resemble humans more closely we will call the technique a failure. IIRC there was a recent paper about giving LLMs more opportunity processing time, and this reduced performance. Same with adding extraneous details, sometimes that reduces performance too. What if eventually everything you try reduces performance? Totally unaddressed.
> It that an insane belief worthy of being a primary example of a community not thinking clearly?
I really need to stress this: thinking clearly is about the reasoning, not the conclusion. Given the available evidence, no legitimate argument has been presented that implies the conclusion. This does not mean the conclusion is wrong! But just putting your finger in the air and saying "the wind feels right, we'll probably have AGI tomorrow" is how you get bubbles and winters.