Why is $AUC=0.5$ and a 45-degree line for a ROC curve considered baseline performance? $AUC=0.5$ and an ROC curve of a 45-degree line often are considered the baseline performance of a model, one that gets absolutely nothing from the features.
If we predict the same (prior) probability of class membership every time, how do we wind up with a 45-degree line for the ROC curve? Either we get perfect sensitivity and zero specificity, or we get zero sensitivity and perfect specificity. The 45-degree line implies that a sensitivity of $0.4$ is possible when the specificity is $0.6$.
How does that happen?
And why, with the ROC curve being so funky, do we say that $AUC=0.5$ is the baseline performance? Is this related to how AUC is related to the Wilcoxon test (Harrell’s concordance index) and not just the geometry of the ROC curve?

When it comes to AUC, baseline performance means the performance of a model that has the same distribution of predictions for both classes.
From this, the diagonal line and $AUC=0.5$ follow naturally from the usual definitions.
If you want to make an argument related to a model that outputs the same value every time (something related to my thoughts on the baseline performance in $R^2$-style statistics that I discuss here, here, here, and here), then you can view it this way, which is how software, such as the pROC::roc function in R, seems to work when given distributions with just one value.
Picking a threshold above that single value being predicted every time results in $TPR=TNR=1$, and picking a threshold below that single value results in $TPR=TNR=0$. Now connect those two points with a straight line (one of many options, but the simplest option and how I would expect software to interpolate) to get your ROC curve. From that diagonal line, $AUC=0.5$ follows immediately.
