This idea has been done before, but it's what popped out at me.

When I thought "what would it do", I came back to the idea of meta-types of creature types. I doubt they could be shoehorned into magic now, and would almost certainly be a bad idea on complexity grounds, but I was interested in how it might work.

The creature types are already an approximation, designed to balance between being flavourfully specific, and usefully inclusive. You could imagine a world where all bird cards had falcon or eagle or phoenix as creature type, and you were just expected to know they were included in "target bird". If the number of types was kept reasonably sensible and they didn't give in to the temptation to codify every possible combination, you could print one (or two) types in small print at the bottom of the text box or something: you're expected to usually know that a zombie is undead, or a soldier is martial, or kraken is a seamonster, but if you're not sure, you can look at card.

Don't read too much into the choice of subtypes for "undead" -- it would make sense if there was such a category, but because there hasn't been in the past, it's not clearly defined. "spirit" includes some things that are more like elementals. Werewolves are traditionally "undead"-y, but are not usually actually dead come alive again. It probably couldn't be fixed cleanly now (and probably doesn't matter).

Missing Devils, but some Innistrad flavor text seems to think that Devils are made of desire, not death. Also, Skeletons, Wraiths and maybe Shades.

Demons aren't undead...

Yeah, wraiths and shades should be in, and probably Skeletons.

The reason for demons is that although they aren't undead they are commonly raised by necromantic magic and commonly exorcised and otherwise affected by holy stuff, so I guessed many of the undead-affecting cards would want to affect them. I agree "undead" may not be the perfect term (and it may be better to go with the simple option).

I agree it's weird to distinguish between devils and demons, but in magic demons seem more often spirit-of-evil-y and devils more often seem physical?

In Magic devils and demons are very different things. Demons are spirits of evil or dark power, while devils are more like imps. You might have one demon be lord over a thousand devils.

Another use of creature types would be to say that anything that's a chimera is also automatically a lion dragon goat :)