Suitably modified, they can. Bayesian neural networks provide uncertainty quantification. The challenge is calibrating the predictions, and deciding whether devoting model capacity to uncertainty quantification would not be better spent on a bigger, uncertain model.

https://en.wikipedia.org/wiki/Calibration_(statistics)

Example: Efficient and Effective Uncertainty Quantification for LLMs (https://openreview.net/forum?id=QKRLH57ATT)