Now consider the fact that an arbitrary other app can take a screenshot clandestinely, via API. Would you like it to happen when you're looking at the summary of your accounts? your list of credit card numbers?

The problem is that certain actions should only be acceptable if initiated by the user, physically. Think of the way Ctrl+Alt+Del works in Windows. This, of course, is not possible if you don't have enough fingers for the action, or something; here comes the loophole of assistive technologies, widely (ab)used for that on most platforms.