Should the phone identify those things and automatically blur out all of the sensitive information in those photos too?
I’d prefer if my phone did neither that nor told the apps that a screenshot was being taken nor allowing the apps to hide anything that was on screen when a screenshot is taken.
It’s my phone, I want to decide what I take photos and screenshots of.
That's the crux.
Yes, it is unreasonable, because scams have proven to be just as effective at getting people to just read the details out over the phone line, and bank these days are not showing much sensitive information in the open anyways (my recent annoyance - someone thought it's a good idea to never show the full account number on screen, showing just first and last few digits, and an option to copy to clipboard...).
Meanwhile, those very apps tend to be ones people would most often want to screenshot for legitimate reasons - e.g. to communicate or make a record of specific transactions, accounts, their states, metadata, etc. None of which is copyable text in the app, and most of it isn't even properly exportable, so it's not like there's any other way.
Done.
Just do a security alert pop up "You are screenshotting potentially sensitive information, are you sure you want to continue".
Imagine having to type "I want to get hacked" on a keyboard layout which randomizes with every character.