Split outlets and the code for them are a new-to-me concept, as i am on a different continent. So excuse the dumb question: isn´t a double neutral feed required for those, as the gauge needs to match the cross sectional area for the live wire anyway?
As you said, the two live wires would be 180 degrees out of phase, so when both are in use, the current in the neutral would subtract, not add. A single neutral is all that's required, and it is the same gauge wire as the two live wires.
The electrical code in the US has become more strict in this in recent years. They call this a "multi-wire branch circuit," and you used to be able to legally run it off two separate breakers in the panel, of course making sure that they were on opposite legs of the incoming service. But now those breakers are required to have at least a handle tie, so one can not be shut off without also shutting off the other.
Personally, I still like the idea of using multi-wire branch circuits, for conservation of resources and operation of the circuits with lower voltage drop. Particularly in a commercial setting with wires running through conduit, if you follow the code requirements on de-rating ampacity when you have multiple conductors in the same conduit, you can really save a lot of materials if you use multi-wire branch circuits. For instance, on a 3-phase system, 3 circuits can share one neutral and only count as 3 current-carrying conductors (because the neutral current cancels out, at least when driving linear loads that don't introduce harmonics). But if you ran each of the three circuits with its own neutral, you have to count it as 6 current-carrying conductors, and then you have to increase the size of conductor because you have to de-rate the amps rating when you have so many conductors in one conduit.
NEC Table 310.15(B)(3)(a). Then you have to increase the conduit size because the conductors are bigger.
The Code has been evolving towards prohibition of multi-wire branch circuits with shared neutrals. Many electricians and electrical system designers now like running each circuit with its own neutral for greater reliability (not having to shut off multiple circuits to work on one) and less danger in case of an open neutral.