Note that any good binary classifier (like "this is AI writing" for Pangram) should maximize the following four probabilities:

1. P(actually true | predicted true) (= true positive rate, recall, sensitivity)

2. P(actually false | predicted false) (= true negative rate, specificity)

3. P(predicted true | actually true) (= positive predictive value, precision)

4. P(predicted false | actually false) (= negative predictive value)

If you just try to minimize the share of false positives, you are only maximizing 1.

The measure which maximizes all four values is the binary Pearson correlation, also called "phi coefficient" or "MCC". It is 1 if the classifier is always correct, 0 if it guesses randomly (its predictions are statistically independent of the facts) and -1 if it always predicts the opposite of the true value.