This article gives examples of information gained by using ordinal over binary response variables. This is done by showing that for the same sample size and power, smaller effects can be detected
Misinterpretation of P-values and Main Study Results Dichotomania Problems With Change Scores Improper Subgrouping Serial Data and Response Trajectories Cluster Analysis As Doug Altman famously wrote in his Scandal of Poor Medical Research in BMJ in 1994, the quality of how statistical principles and analysis methods are applied in medical research is quite poor.
I discussed the many advantages or probability estimation over classification. Here I discuss a particular problem related to classification, namely the harm done by using improper accuracy scoring rules. Accuracy scores are used to drive feature selection, parameter estimation, and for measuring predictive performance on models derived using any optimization algorithm.
Optimum decision making in the presence of uncertainty comes from probabilistic thinking. The relevant probabilities are of a predictive nature: P(the unknown given the known). Thresholds are not helpful and are completely dependent on the utility/cost/loss function.