While I agree, we can always have multiple overlapping error bars to understand how the probability is distributed. I am not sure how a probabilistic forecast method is able to perform this better because the confidence interval is always generated through sampling in either situation.
Though probabilistic forecasting methods may have a Bayesian approach, it is Monte Carlo sampling that helps generate the confidence intervals.
Though probabilistic forecasting methods may have a Bayesian approach, it is Monte Carlo sampling that helps generate the confidence intervals.
Feel free to correct me if I am wrong! Thanks :)