I'm struggling to see what the problem with the idea of wave function collapse is.

In the diagram pictured, the probability of the ball landing in each of the cylinders is described by the normal distribution. Once the ball has reached one of the cylinders then the probability distribution is 1 for that cylinder and 0 for everywhere else.

Likewise the wave function describes the probability that a particle will be in a given position. Likewise it also collapses when it is measured.

What's the difference between the quantum theory and the analogy?