Are Staryu and Starmie the only Pokemon that don’t have eyes, or any discernible kind of face? If so… why? (In-universe explanation and/or designers’ perspective explanation welcome)
They’re not quite the only ones. Regirock, Regice, Registeel and Regigigas don’t have faces, just arrangements of dots (possibly eyes or some other all-purpose sensory organ?). Those do look as though they should stand for faces, but you can sort of say the same thing about Staryu and Starmie’s cores. Roggenrola has a thing that sort of looks like it should be an eye, but if you actually read the Pokédex is more a sort of… huge forward-facing ear? And it’s not clear to me whether that counts as a face or not. A couple of the Ultra Beasts don’t really have faces as such, but perhaps we shouldn’t count them. A few others arguably have only parts of faces – like, Zubat kinda just has a big gaping mouth, and Magnemite and Sigilyph are just single eyes. It’s not clear to me how many faces Claydol should be counted as having – 0, 1, 2, 4 and 8 all seem like acceptable answers to me. I find it difficult to think of Unown or Beldum as having faces. Certainly Staryu and Starmie are unique amongst non-legendary Pokémon, and unique among Pokémon of the first two generations, in having no facial features at all. From the designers’ perspective, not giving something a face is a good way to make it seem alien and inscrutable, because humans express emotion through our faces and it’s hard for us to relate to something that doesn’t appear to have one. That’s clearly in line with the design goals for Staryu and Starmie (given their mysterious nature and connections to outer space), the legendary golems, and especially the Ultra Beasts.
As for an in-universe answer… well, I suppose we should think about that by looking at animals in the real world. Most animals don’t have expressive faces in the way that primates do, but a lot of them – even many invertebrates – have a mouth and a cluster of sensory organs located near the brain [EDIT: or what passes for a brain in simpler animals]. And ultimately that’s probably just a matter of common ancestry, not a question of faces being somehow an optimal way of arranging those particular parts of a body. I’d be inclined to assume the same for Pokémon, in which case we might think that – like real starfish – Staryu and Starmie belong to a line of descent that split from ours a very long time ago, or even that they really are extraterrestrial, as the games occasionally hint. What’s maybe more interesting about this whole line of thought, though, is that almost all Pokémon have expressive faces that allow them to show emotion in ways that are more or less intelligible to humans and to each other, with a little effort. The out-of-universe design reason for this (Pokémon are supposed to be relatable, and most gamers are human) is strong enough and obvious enough that we oughtn’t put too much weight on it, but maybe you could read it as saying something about coevolution and interspecies cooperation in the Pokémon world – they are all somehow helped by having means of nonverbal communication that work across many species.