Pretty sure it's quite the opposite of what you're implying: People see those LLMs who closely resemble actual intelligence on the surface, but have some shortcomings. Now they extrapolate this and think it's just a small step to perfection and/or AGI, which is completely wrong.
One problem is that converging to an ideal is obviously non-linear, so getting the first 90% right is relatively easy, and closer to 100% it gets exponentially harder. Another problem is that LLMs are not really designed in a way to contain actual intelligence in the way humans would expect them to, so any apparent reasoning is very superficial as it's just language-based and statistical.
In a similar spirit, science fiction stories playing in the near future often tend to have spectacular technology, like flying personal cars, in-eye displays, beam travel, or mind reading devices. In the 1960s it was predicted for the 80s, in the 80s it was predicted for the 2000s etc.