Can we not use these cop out words like "probably"? Will it or will it not? If you don't know just say you don't know.
I’m not going to say one way or the other because, as I said, this is a poor model for a bicycle wheel. Just poking a stick or rod or anything into the ground (or something else) isn’t anything like a bicycle wheel in a corner. If you need another model to consider, think of a broom or a hoe or even poking the spear into something and picking it up. In other words, put a lateral force on it.
But anyway I don't have a problem if you want to change the stick to a different object. The physics are all the same. However when you say you apply force to the broom, it sounds like you're saying you're using both hands. One hand at the end of the handle, a second hand in the middle of the handle. That's not accurately translating the scenario I gave you. I told you you could only apply force to the top point.
Again, where on a bicycle do you push down on the wheels during cornering with only an axial load? Do you agree that a bicycle wheel undergoes centripetal force in a corner? That’s a lateral force that you say doesn’t exist.
If you didn't hold the middle of the broom, but instead only pushed down on a LEANING broom at the very top of the handle with your palm, (1) would the bristles still ALWAYS collapse in the same direction, under your belief system? Or would it collapse randomly in either direction every time your try? (2) If you think it will always collapse in one direction, which direction is that? Concave side or convex side toward the ground?
Please answer the labeled questions.
If the broom is new with no previous curve imparted through use, the bristles would collapse in every direction. If you did it over and over again
with the same broom, a pattern would eventually develop but that is because the damage of the initial collapse would introduce a weak spot that would bend in the same place upon each subsequent collapse. But if a new broom is used each time, predicting the direction of collapse of any individual bristle would be impossible.