This situation is presumably like the double-slit experiment: any surviving record at all anywhere of the specific path taken breaks the superposition that exis

This situation is presumably like the double-slit experiment: any surviving record at all anywhere of the specific path taken breaks the superposition that exists between the configurations where different paths were taken. Superposition only works when the result of multiple configurations (where different paths were taken) are exactly the same (besides their quantum amplitudes). Quantum algorithms rely on superposition in order to do better than classical algorithms.