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?
 A: 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.
A: For notations, ROC AUC is some metric to measure the quality of binary classifiers (assigning 0 and 1), that return for each case some score $s$ indicating how much the classifier favors this case to be considered as 1.
First, I am not sure what you refer to by "hump", but keep in mind that the ROC curve can only go up and to the right, so there are no real humps.
Second, maybe you think of two ROC curves, where the first has larger ROC AUC, but the second one is crossing the first one at some point, such that it is "above" the first one. But note that "being above another curve" is not really a sign of quality, e.g. completely random classifiers can be, more towards the right or the diagram, above a good classifier.
The very point of ROC AUC is that you have a metric that is independent of a threshold for $s$. Imagine some anomaly detection method $C$, which scores all measurements with the score $s$, indicating how likely $C$ considers them to be anomalies. Now, the standard way to work through the results is to first investigate the cases that are most likely to be anomalies, and then work your way down as your time permits. Note, that you don't use a threshold here. You cannot do this with classifiers that only give you a binary result, because you don't know which is most likely to be an anomaly. But you can do this with classifiers that return a score. And ROC AUC is a metric that compares this capability of classifiers. A scoring classifier is better if it shows you the real anomalies first. And that is exactly what ROC AUC measures.
But it always depends on what you want. If you want to turn a classifier, that returns scores, into a classifier, that only returns 1 or 0 depending on whether the score $s$ is above or below the threshold, because you as a domain expert know that this is the exact threshold to use and no other would be correct, then you shouldn't use ROC AUC.
