As I was growing up, my family had a couple of sayings I took for granted were universal, at least within my language. As I became an adult I have learned that these are not universal at all:
the ketchup effect. It is an expression meaning that when things arrive, they all arrive at the same time. Think of an old school glass ketchup bottle. When you hit the bottom of it, first there is nothing, then there is nothing and then the entire content is on your food.
faster than Jesus slid down the mount of olives. Basically a saying that implies that the mount of olives is slippery due to olive oil and Jesus slipped.
What you lack in memory, your legs suffer. An expression meaning that when you are forgetful, you usually need to run back and thus your legs suffer.
Vigorous shaking mixes the thicker areas (where the sauce has settled) and the thinner (more watery) areas so they now have the same viscosity (pouring characteristics). Most importantly, this lets the mass of sauce slide cleanly down the bottle, helping the air bubble to also slide up in one unit at the same time, preventing the “air-lock” blockage at the opening.
Important Note: Before vigorously shaking any container, ensure that the cap is truly secured!
Now you are in control!
I think what you said is true but that also ketchup as a material is shear thinning—meaning as you shake or tap the bottle, this creates stress or “shear” on the liquid which causes the viscosity to decrease. It also takes a little bit of time for the liquid to re-thicken, so it will actually pour pretty well a few seconds after shaking it.