Why can’t psychic types, or at least some of them, eat things that have/had emotions? What would happen?

Psychic abilities tend to be stronger when the psychic in question is in physical contact with a target. Thus, imagine putting your mouth on something, only to hear the last dying scream of a once-living entity.

That’s why psychics generally prefer vegetarian lifestyles. Or at least the ralts line does. Many other psychics tend to have less potent empathic abilities (or aren’t quite as concerned), so eating meat or the like is less of an issue with them.