But collapse interpretations require additional non-local algorithms

Not for computations, they do not. If you try to write a code simulating a QM system, end up writing unitary evolution on top of the elliptic time-independent SE (H psi = E psi) to describe the initial state. If you want to calculate probabilities, such as the pattern on the screen from the double-slit experiment, you apply the Born rule. And computational complexity is the only thing thing that matters for Occam's razor.