Honestly it’s pretty reasonable for Psychic-Type to be in the position it’s in. It’s always been a weird type, since it doesn’t “fit” the two main categories of type. Most types are either elemental (fire, ice, water, electric, etc.) or physical characteristics (rock, bug, grass, dragon, ghost, etc.) or occasionally both (flying). The others that don’t really fit either — Dark and Fairy — are later additions than Psychic where its identity had already been formed.
Psychic-Type is basically Normal-Type except abnormal. These are mons that don’t fit either of the above categories, but can do ooooh psychic powers ! Bend a spoon ! Use the undescriptive attack Psychic to hit hard all, y’know, psychicly!
Because of that it’s not got a lot of instinctive type interactions that necessarily track. It probably could resist and/or be super effective against Normal, and they didn’t go for that, but that would also harm Normal a lot so fair enough. For all the others… what does using “Psychic” on a flame, or an ocean, or a plant, or a rock, etc. really do? Psychic is so undefined as a concept or element that it wouldn’t do anything. Being Psychic isn’t real, it’s just being vaguely special. That extends up to current day. Psychic Fangs is just Bite but Psychic, Psyshock is just Psychic but shocking(?), Psycho Boost is just Psychic but it, ironically, lowers your own stats (so not boost then).
When you take that into account, Psychic as a type pretty much sucking due to lack of meaningful interactions tracks, it’s much like Normal-Type in that way. But Psychic-Type is meant to be more special than Normal-Type, so give Psychic Pokémon some higher stats on average and pat yourself on the back, you’ve got a realised type concept. I think it’s why the vast majority of Psychic-Type Pokémon are mammalian. Obviously there’s some exceptions, just like Normal-Type has some exceptions (such as God or dragons except old), but on the bulk these are supposed to be real life everyday animals that are just turned into Pokémon with maybe like one or two fantastical components added to them. Gen I only had Psychic-Type mammals and a tree (and a clone of one of those mammals but it’s still a cat). Mimes are mammals too.