Every neutral needs to stay with its partners hot(s) in the same cable. You can't have promiscuous neutrals. There are a bunch of reasons, but let's just touch on a few of them.
Neutrals don't have breakers. That means, say, a hot/neutral pair rated for 15A will have its hot wire on a 15A breaker, and the neutral is assumed to be protected since how can the neutral flow more current than the hot? Well a promiscuous neutral could be returning its own 15A plus another 15A from another circuit; overloading at 30A. Nothing would prevent this.
EMF imbalance causes eddy currents and wire movement. A single wire carrying AC power throws up a lot of EMF. A reed relay laid alongside a wire will actuate if current flow is > 10 amps. They intentionally wrap wires in loops big enough for ships to sail through, and test EMP resistance and degauss ships. It can also cause "eddy current heating" in anything metallic that isn't specifically laminated to avoid this. The pulsing magnetism can also cause physical vibration of the wire in the walls, which can fatigue and break the wire, cause arcing. Arcing can set things on fire inside the walls where the homeowner can't detect it or put it out while it's small.
However, when all the wires in a circuit run together, it means currents are equal and opposite among the wires, and the EMFs cancel each other out, which eliminates the above problems. Since current flows in loops, that's guaranteed to happen as long as all the wires in that branch of the circuit are in the same cable. So it's a code requirement that all wires in a circuit branch run together in the same cable or conduit.
GFCI/RCD's don't permit cross-wiring. They work by detecting unequal currents, using the abovementioned "EMFs cancel each other out" trick. A promiscuous neutral will obviously cause unequal currents and guarantee a GFCI trip. That means using this very sloppy wiring technique will backfire on you badly if you ever upgrade the circuit to GFCI protection.