Oh I get that experiments prove out. What has always been unintuitive to me to the point of seeming wrong is that said spin is random and lives in a probability cloud that is probabilistic only until we observe it.
The math works and the experiments work, but it feels like a broken clock situation. It happens to correlate well, but the understanding and models are missing something in the actual underlying physics that, if understood, would throw the whole randomness part out the window.
> [the] spin is random and lives in a probability cloud that is probabilistic only until we observe it.
My mental model of it is kinda reversed. The maths assign a specific, deterministic state to each electron between each measurement. However, the "left" state is equal to "(up + down) / sqrt(2)". It then follows that when we measure an electron that is in the "left" state along the vertical direction, we get 50% up and 50% down: the probabilistic behavior happens when measuring, which "forces" an electron that was in the "left" state to become either "up" or "down".
I agree though that it would be less frustrating if there was some property of the electrons that would allow to predict in which state it'll collapse.