On the other hand I think we would be justifiably irate if it turned out that the Post Office was photographing every single postcard and processing the information it contained into a permanent database.
Except that it turns out that the Post Office is actually doing that. It is photographing EVERY piece of mail and processing the information and putting it into a database. I did not examine the articles closely enough to be sure, so I do not know if that includes evaluating what is written on postcards. I suspect not, but I also suspect that the information contained in the article would not have answered the question of whether they do or not.
Postcards are *supposed* to have a designated address area, and a designated text area. That being said, people write all over the whole thing. It can lead to some mis-sorted mail if the address recognition software happens to recognize some of the text instead of the address. The post office does indeed collect images of the front (address side) of all mail, that's how it gets sorted. (OCR, and if the computer can't read it, it goes to a graphical display for a human being to decipher).