Reminder to everyone who will not listen anyway: Eeveelutions are not intentionally all special Types, it is just a coincidence.
The basic premise of Eevee is that it evolves into many different Types. Most of Eevee's Types are all classical elements. It's just the most straightforward way to showcase the concept of a fantasy organism with radically different split evolutions. The Gen 1, 2, and Gen 4 Eevees are all classic RPG elements, THAT'S why they are special Types. Media usually shows elemental powers as firing beams of elemental energy or whatever. Eevee are not special Types on purpose, they're RPG elements. And THOSE overall just tend to be non-physical in nature.
Espeon is Psychic, but this is actually just an extension of the elemental thing. The Gen 2 Eevees are still adhering to the RPG elements thing, but Gold and Silver were originally designed with the intention of being the last Pokemon games. So they tried to make the 2 "ultimate" elements, light and darkness, into Eevees. Psychic is just being used as a stand-in for the Light element in Espeon's case. It was originally white, not purple. It's supposed to be the Light elemental.
Don't you fucking dare quip at me that Dark Type is not the darkness Type, you motherfucker. You're wrong. Umbreon is the darkness elemental and there are countless reasons why Dark Type and darkness are related. Dark and Ghost BOTH are the "Darkness Type" they just do it in different ways.
And lastly, Fairy Type is not a special Type, I don't give a fuck if it "would be", it has never fucking been a special Type. The Eevee designers do not intentionally adhere to your arbitrary bullshit.
They broke the elements thing to market Fairy Type, but if they continue with the elemental concept then Flying and either Ground/Steel/Rock are the next ones in line. They could also do Poison. It's not a traditional element, but Pokemon treats Poison Type as tho it were some weird purple ooze element.