How is AUC helpful when we only need one threshold of a classifier AUC is a summation of performance at different thresholds, but do we only care about a good performance at one threshold?
Imagine a classifier with a low ROC but shots up at point of a low FP and high TP, is it better than another classifier with a higher and smooth ROC?
Maybe a more reasonable example: classifier A has a larger AUC with fuller and smoother ROC, while B`s ROC is flatter but has a hump. Which to choose?

If you are using a 2-class classification model which outputs a likelihood of datapoint being in positive class, then the ratio of True Positives (TPs) and False Positives (FPs) will only monotonically increase with the increase in the threshold value, for any sane model.
Since this likelihood can be any real number between 0 and 1 in our setting, intuitively, it is expected that the ratio of TPs and FPs will also increase smoothly as the likelihood increases. So any spikes or sudden/sharp increases in ROC are not a very good sign. It is undesirable that the performance of a model drastically changes/decreases with only slight changes in threshold, as it can impact the stability of the resulting predictions especially if such models are put to production.
