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The role of the "observer" in quantum theory?

I've been reading about different ideas of getting the observer out of quantum theory. One Sean Carroll seems to like is Everett's many worlds concept.

I had a thought that I need someone here to shoot down. It could be something as basic as the double slit experiment that proves me to be wrong. Here's my thought:

As I see it, we never really "measure" the position of something. We sense a photon that is emitted by what we are "looking" at. Why couldn't the wave function of a particle just break down at the moment it emits the photon at a specific point in space-time regardless of whether there is an observer or not. After the emission, the particle location would go back to being a probability function.

What am I missing?