In the age of cheap, wireless chip+pin terminals, I think that the rite of taking the card to The Secret Room Where The Bills Are Printed is merely a show stage

In the age of cheap, wireless chip+pin terminals, I think that the rite of taking the card to The Secret Room Where The Bills Are Printed is merely a show staged for status reasons: the patron gets to show off confidence (as in the original con trick) while the restaurant gets to show off how much patrons trust them. The first restaurants breaking that line would come off as not sufficiently trustworthy, taking a completely unwarranted reputation hit. It must be a well known paradox, the more you expect people to trust you, the more they will be inclined to trust you.