Selecting a boundary on a binary classifier to optimal precision and recall

The intersection of the precision and recall curves is certainly a good choice, but it's not the only one possible.

The choice depends primarily on the application: in some applications having very high recall is crucial (e.g. a fire alarm system), whereas in some other applications precision is more important (e.g. deciding if somebody needs a risky medical treatment). Of course if your application needs high recall you'd choose a threshold before 0.6, if it needs high precision you'd choose a threshold around 0.85-0.9.

If none of these cases apply, people usually choose an evaluation metric to optimize: F1-score would be a common one, sometimes accuracy (but don't use accuracy if there is strong class imbalance). It's likely that the F1-score would be optimal around the point where the two curves intersect, but it's not sure: for example it might be a bit before 0.8, when the recall decreases slowly and the precision increases fast (this is just an example, I'm not sure of course).

My point is that even if it's a perfectly reasonable choice in this case, in general there's no particular reason to automatically choose the point where precision and recall are equal.