Well thanks to physics and an inside source, I have found an answer to this age old question. The reason they do this is to prove that, like the original marketing said, it's not just milk and soft serve. They stick a spoon in the Blizzard, flip it upside down, and if the spoon stays in position, it means the Blizzard is properly made. If it slips out, or the ice cream falls to the ground, it means that the soft serve is not yet ready for consumption. It's basically a way to prove to the customer that they're getting the best product for the best money.
So DQ is using a coefficient of friction to determine whether their ice cream is up to scratch. The spoon or ice cream falls out, the coefficient of friction is not high enough. The spoon or ice cream remains unmoving, it's up to scratch. But one more physics property could explain this, could it be a vacuum/ suction between the bottom of the cup and the small liquid layer at the bottom of the ice cream? It's for you to decide, but a blizzard tastes great to me regardless of it staying in the cup or not.