Thing is, it's not that the pokes that get it shouldn't. It's that plenty of ones that should get it don't. I'd expect a learnset like Wonder Room or Telekinesis, where basically any psychic type or magical poke* can get it. Instead it's basically only Psychic birds. Noctowl is fine, but Beheeyem has at least as much justification for the move and doesn't get it, and I can't see why that is.I'm not convinced that there's an inherent association with bird Pokemon - just that those Pokemon that get the move happen to be bird-like. "Suggestion" is an odd word in this context but throws up associations with illusion and telepathy. Most of the Pokemon that get Psycho Shift tend to be ones which use their psychic (or Dark, Fairy, etc) powers for these purposes rather than manipulating the elements, and learn similar moves that mess with the opponent's stability or perceptions.
...
Though I'm surprised that the Ralts line doesn't get the move, nor Audino - they're strongly linked to empathic powers of that nature.
*Ghosts, Delphox, Golduck, etc