In my experience as well using logprobs to try to quantify uncertainty, LLMs are a poor fit. Neural nets in general struggle with 'calibration' --- ie. if a prediction is truly 50/50, neural nets are often prone to predicting overconfidently [0].

I ran some tests using GPT-4 to do some basic classification a couple years ago. On ambiguous options which had to be escalated to a human, the LLM would regularly output something like a 99.8% probability, compared to 99.99% for a correct answer.

0: https://arxiv.org/pdf/1706.04599