Not easy to always say what the benefit is: if you present in-model uncertainty from a stochastic model that might still say nothing about an estimation error v

Not easy to always say what the benefit is: if you present in-model uncertainty from a stochastic model that might still say nothing about an estimation error vs the actual process. For forecasting to show actual uncertainty you need to be in a quite luxurious position to know the data generating process. You could try to fudge it with a lot of historical data where available - but still...