[modeless]

The future is now. Android has been doing this for years and it's awesome. There's no text you can't copy.

To clarify, by default copy and paste works the normal way, but you can open the app switcher to use the OCR copy/paste which works on non-selectable text too, even in images.

[QuercusMax]

There's a way to prevent this - to my great annoyance, health apps (such as the ubiquitous MyHealth variants) and banking apps can prevent you from taking screenshots or copying text. This is presumably to prevent screen-scraping apps from stealing your private data, but it's really annoying when you're trying to screenshot a QR code for some kind of check-in process.

[checkyoursudo]

That's why you need a second phone to photograph the screen of the first phone.

[josephcsible]

If you root your phone, you can use an Xposed module like DisableFlagSecure to get around apps that do that.