Buccee's could hand deliver their barbecue to my car in the parking lot and I still wouldn't try it again.
I would bet the rebuttal from CFA would be that takes away some of the freshness of made to order food. No matter how fast you're moving it, something is going to stay out on the line longer than they would like. That said, what you described is how CFA (and other fast food outlets like Burger King) delivered food at the student unions at UNT and UTA many moons ago.
You need to use their app for ordering if you go there with any frequency. It's never let me down and you get free stuff.