If you're using "character psychology" to describe the internal mechanics of a character - how they think and feel about things, why they think/feel that way, how they change over the course of a story, and what sort of psychological state this indicates - then yes, I think it should be a priority, at least for central characters.
It's fine to define a secondary or tertiary character by their function in the plot - they can be "guy in marketplace who gives directions" or "girl in town who is keeping secrets" without issue - but when it comes to central and/or main characters, it's worth investing some time in getting to know them from the inside out as a creator, and then choosing how much of it to include in the story.
I might be a bit biased in this - my comic tells the story of someone who is recovering from an old trauma, and still dealing with its consequences (magical consequences, because magic!) - but I feel it's definitely something worth considering.