How come when I apply a full helm to an Argonian in the CS, it shows up on them without issue, but in-game it doesn't work?

The CS doesn't run full mechanics/checks on NPCs or the various components that make up one. It does basic sanity checks, nothing more (and in the case of first person hands, a bit less).

I see. It's always been my understanding that helms fit over the head mesh (since when setting them up in NifSkope, that's how it is), full or open-faced, and so having a full helm over a head with a protruding snout would result in the snout sticking out of the helm. That is correct then? Because that isn't what happens in the CS, at all, I put a bonemold helm on an Argonian and it was as if a Dunmer something was wearing it.

That's because beast races can't wear full helms or boots. Full helms also may replace the head, although I'm foggy on the details there.

I'm sure some of them do that, based on looking at the back of my character so many times and not always seeing the back of his thick, green neck with every helm he wears.

AFAIK there are two types of helms in Morrowind - the ones that only replace your hair, and the ones that replace your hair and your head. While the former can be worn by anyone, the latter may not be worn by beast races. I believe this restriction is hard-coded.

You can see which body parts a helm replaces in its properties window. If the head body part is set there (even if it's empty), beast races cannot wear it. Similarly, beast races may not wear any shoes or boots that replace the left foot or right foot body parts.

Thank for this info, it shall certainly come in handy. I already knew boots had to take up the ankle slot for beast races though, having worked with Quorn's Argonian Armor.