In a way, every point estimate or threshold is "arbitrary" in the sense that it and its consequences are indistinguishable from nearby point estimates/threshold

In a way, every point estimate or threshold is "arbitrary" in the sense that it and its consequences are indistinguishable from nearby point estimates/thresholds. So in statistics people usually pick a threshold based on some reasonable risk function and some utility function, and call it a day (but it's important to be clear which functions are being used!). Since there is rarely one right threshold, it is pointless to look for one, but also pointless to complain that the one that was chosen was arbitrary. Unless, of course, it is so far off as to be noticeably less useful in making decisions, and making good decisions is, after all, the whole point of point estimates and thresholds in decision theory.