I think the chips/fries with ice cream thing is the salt/sweet factor. When I was little and we'd go for fast food, I would always take a gulp of my ice cream shake while chomping on the fries. Speaking of salt/sweet, I also make tuna salad sammies with (horrors) Miracle Whip, which is sweeter than mayo, and smush chips in that.
Reason I found this thread was curiosity about what chips people pair with what...never realizing there were so many people who smush them in sandwiches like me! Today I decided on sour cream and chive chips with pulled pork. OH YEAH.