Perhaps that is true, but the average flies-twice-a-year-traveler won't see it that way. Delta needs leisure travelers just as much as they need the road warrior and screwing people over in this way creates significant negative will against a brand - and I can guarantee you that Aunt Jane will complain when she makes it to her family reunion after getting screwed over.

It is one thing to tell a passenger they can't pick a seat or get charged to carry on a bag. To tell a passenger that they won't get taken to their destination because of a small mistake or unexpected issue is not going to be well received. People have an expectation of what it means to fly on a legacy carrier, and stuff like this is part of that expectation. Putting someone on standby costs Delta no more than a few bucks for a bag of peanuts and fuel for the extra weight and would be worth it from a brand protection standpoint.

It is certainly well within Delta's rights to refuse rebooking of the passenger. I just think it's ill-advised in the long run. Delta won't out-compete Spirit being Spirit and they shouldn't try to (although I'll note that I've heard good success of people getting flat tired on Spirit in the past - admittedly anecdotal but somewhat ironic relative to what one might expect).