It is only unpredictable if you confine yourself to a single branch. If you embrace Many Worlds and simulate things accordingly, creating branches as needed, the result of such simulation is consistent and reproducible.
Wavefunction collapse has no 'woo'. It's simply the application of a non-commutative operator. Many worlds has 'woo' because it supposes the existence of infinitely many unobservable worlds. Thomas Aquinas question of how many angels are on the head of a pin seems to be a more fruitful exercise. At least the head of a pin can be given a quantified size. On the other hand, no one can tell you where these multiverses exist. How they exist. What measure they occupy, or anything else. They are as unreal as angels. Unless you believe in them (which is fine, just admit it).