Not mentioned: Code also sets minimums and maximums. The neutral can't be smaller than the ground and does not need to be larger than the phase conductors.
There are some twisty parts to the logic. Everywhere else you must size to 125% of the continuous load plus 100% of the noncontinuous load. But with neutrals, 210.19(A)(1) and 215.2(A)(1) change it to 100% of both. So if you are running the normal ampacity calculations for the phase conductors, the neutral result might be slightly different. That's on top of the 70% reduction above 200 A. I'm not sure why THAT reduction matters though if you are already planning on a 200 A service since the load would be less than 200 A.
Ignoring any true 240 V loads or the reductions for ranges and so forth we are sitting on a calculated load of 200 A. If however you do any of those reductions at all you end up a little lower. If it was exactly 200 A load then you'd be looking at a 3/0 neutral on the 75 C column or just barely 2/0 on the 90 C column. However taking any of these reductions at all into account gets you down to 2/0.
AND just to make it near impossible to correctly reduce the size of a neutral, Code mentions harmonics and suggests to accommodate them or at least not reduce the size of the neutrals when harmonics are present. Residential doesn't seem like a harmonic rich environement but the power supplies for ALL electronics are very harmonic rich: computers, UPS's, solar inverters if you have one, car chargers, HVAC fans and compressors, pool variable speed pumps, etc., all rich in harmonics which could cause an undersized neutral to overheat and burn up. So how do you calculate how much additional current, size, etc., that you need? NEC offers no guidance. In engineering quite frequently you will see references to IEEE 519. BUT if you actually read it two things jump put. The first is that this is not a general purpose standard. It is for utility feeders, not service entrance or general purpose feeders and branch circuits. Second, it sets LIMITS on harmonics, not sizing to accommodate them. There are also some similar things talking about K-factors on transformers with similar nonuseful guidance. So if you can see where this is going, this is why the industrial/commercial practice is tending towards using full size neutrals.
Part of the trouble is the skin effect. As the frequency increases the current tends to flow more along the surface of a cable. At some point the center of the wire isn't even used. In microwave and high frequency work we use coaxial cables and wave guides because the signals are essentially traveling only on the surface of the cable. In aviation they use 400 Hz because it reduces the size and weight of transformers but they have to oversize their cabling.
All that being said I've had 30 years of experience, mostly industrial, with all kinds of crazy power systems. I have never yet experienced an actual bonafide harmonic problem and here is why. Lots of power electronics uses a rectifier for a power supply. So internally the system has a capacitor in series with the diodes in the rectifier. When the line voltage exceeds the capacitor voltage, it starts charging up and we get a current. This ceases as soon as the AC sine wave drops below the capacitor voltage and the diodes block the capacitor from discharging. With a half wave rectifier this happens once per AC cycle but for efficiency reasons we use full wave rectifiers so it happens on both the positive and negative peaks. So we get a double pulse of current or "rabbit ears":
Now that obviously looks NOTHING like a sine wave so the %THD is going to be pretty high. As the power draw increases the rabbit ears are going to widen and it will eventually the current just look like a sine wave with a couple odd looking humps. Along with that, the %THD decreases as load increases. Even in systems with no filters at full load %THD drops down to about 6-10% but at very unloaded conditions it can be well over 50%, meaning that over 50% of the power draw is harmonics. Sounds, scary, right?
BUT this is with CURRENT. Normally we don't know what the anticipated load is so we tend to make sure that we make the transformers, service conductors, etc., plenty large. And as long as the transformer and wiring is not overloaded we will see a "stiff bus"...voltage is almost constant. If however we get close to exceeding the transformer capacity then the momentary surge from a large drive (our rabbit ears) can push a transformer to the point where the voltage momentarily dips. When this happens we get voltage harmonics. That's a bad thing and that's why IEEE 519 exists...to give recommendations on when the voltage (not current) harmonics are too high. To be fair it does give limits on current harmonics but they are in terms of %TDD or "demand". %THD limits on current are in terms of transformer capacitor. So if we sized everything correctly though we should have sized the transformer to handle the highest current draw from the drive, which is the point where the %THD is very low (below IEEE 519 requirements). At lower power draw we don't really care about any of this because the transformer capacity will be there. And that's if it is sized very closely to the loads. And that's not accounting for the fact that most of the time you can overload a transformer without harming it but a substantial amount at least for short periods of time. And the same goes for the wiring as well. So when I get a call for a harmonic problem I just take measurements of the VOLTAGE on the line side. So far I have never found a "harmonic problem" doing this. I have found plenty of POWER problems often relating to undersized or failing transformers, bad connections, bad loads, and surges that are darned near impossible to locate a source for, but so far nothing in terms of harmonics. It seems to be an electrical boogie man. I have no doubt that it exists but if it does exist, it is just going to point back to some other problem such as an undersized transformer.