Is this really that big of a flaw in this implementation? I don't think it's worth the additional complexity to address it. (Encoding depth information in some way, trying to detect "flat" surfaces, whatever).

Discerning a camera taken image of an image is typically very very easy. The collors/exposure/etc will all be obviously wrong in ways to a human, even without doing any analysis.

You mean that it is sometimes very easy. But it is also sometimes impossible. You seem to be thinking only of poor quality photos of poor quality prints, but there's no basis for assuming those characteristics.