Are the 3 wires found in standard NM-B electrical cable functionally identical?

No, they're not 100% identical. The hot and neutral can be counted on as being identical; or in 3-conductor +ground cable the hots will be identical. In larger sizes of cable, the ground is smaller, and in 3-conductor cable, the neutral may be smaller. That's because in large feeders, 100% neutral imbalance is unlikely. For instance 2-2-4-6 is a cable size; #4 neutral #6 ground.

But the hots (or hot+neutral in 2-conductor 3-wire cable) are the same size. If you were wiring a UK device with US wires, you might tape the white to be red (hot) and leave the black as neutral.

Ground, however, is special. It is not simply another conductor, it performs a very different function than than neutral, and that is what makes it reasonable to not give it insulation.

The outer sheath and inner insulation serve many purposes more than you are giving them credit for.

The wire insulation's jobs

Aside from the obvious (insulation and color coding)... the insulation provides protection from abrasion on sharp edges, and when wires are stuffed into a junction box. It also must not burn easily, and must not emit toxic gases if it does. And it must not deteriorate over time (UV notwithstanding).

The sheath's jobs

First is grouping. Grouping is vital to understanding how a circuit works - e.g. if you have a 3-way switch and 2 wires go into one cable and 1 wire into another, you know which ones are the messengers. It keeps neutrals paired with partner hots, which is mandatory and AFCI/GFCI breakers require this. Since currents should be equal, keeping the wires together assures that the wires' EMFs cancel each other out, and with nothing between the wires, it prevents inductive/eddy current heating.

Next is binding and strain relief, as the cable is clamped where it enters the junction box. Clamping the individual wires would create a stress point.

Also stopping nails. The usual rule is that cable is stapled or penetrates at the midpoint of a 4x4 joist, and one should use 1-1/2" or shorter nails so a nail isn't going to reach the staple or hole. But between holes and staples, the cable floats and can come within 1-1/2" of the wall. In that case you want the cable's skin to be tough enough that the nail moves the cable rather than penetrates it.

The cable also must hold the markings which identify the cable type, which decides where it is legal to use based on its characteristics. Color coding is often done - 14AWG being white, 12 AWG yellow, and 10 AWG red.

As I understand it the three wires are the same alloy and same diameter. They are in the same crystalline state. (Formerly the centre wire was smaller gauge, but not now.)

However, I disagree with this statement of yours

If the answer to the above question is "yes," then this would mean that the wire sheathing serves no purpose other than as a canvas to display colors as a means of identification, so that the user can have an immediate visual understanding of which wire should do what. (Otherwise, without a colored sheathing, each individual wire would have to be labeled by the handler in advance, or traced to the source, in order to determine which wire controls what.) Blockquote

The sheath actually performs some practical functions.

@Harper nailed the answer. I would just add that there are some fairly common circumstances where you would want to use a white normally-grounded wire as an energized wire. It's useful to know that the black and white wire are truly identical outside of color and therefore there is no reason to run a separate black wire instead of re-purposing the white one. Keep in mind that the white wire should be re-marked as black (or red, blue, yellow) to indicate that it may be energized.