Just so we understand each other - I never implied he does.
Sure.
Well, then we have a conflict. Penitential psalms often quite clearly put the fault at whoever speaks them. If the "curse" Psalms are nothing but a call for divine justice there would be no need for penitence.
Certain acts and things simply create miasma/negative energy regardless of what everybody after Christ considers morality. For instance- menstruation creates it and it requires ritual purification. Leviticus is clear it requires a "sin offering" to rectify. Note that this isn't unique to Old Testament- similar purity requirements are seen in other religions around Mediterranean. Yet, menstruation is a natural and proper biological function, not under control of woman and is essentially amoral. Yet it still creates "sin".
Violence also creates it. A lot of violent thoughts and violent speech will create it, even if used in "justified" imprecatory prayer.
Let me rephrase: people are easily deceived, and this includes self-deception. There are for example quite some protection rituals in circulation that simply don't work, it's just in the best interest of whatever they're protecting against to pretend they work. Similarly, a person who has brought upon themselves divine wrath (or, in less mythological language, hurt themselves spiritually) might by this very fact lack the clarity to distinguish the source or even existence of the curse.
Something like reading Psalm 51 bringing down divine wrath would not go unnoticed by people. Have you ever witnessed a curse or at least accumulation of considerable amount of negative energy?
Depression and anxiety out of nowhere, stuff breaking down, stuff keeps falling out of your hands, plants around you dying, suddenly feeling like you're coming down with the flu or even developing mystery illnesses, getting fired, everybody pissed off at you for absolutely no reason. Even staunch atheist begin to complain "It's like I'm cursed or something."
Protection rituals that don't work can fly below the radar because they aren't tested. They simply don't do anything, but because the person isn't getting actively attacked by anything there's nothing to protect against. This is different from something that has an actively negative effect.
I care about occultism and expanding its knowledge base. Psalms are often used amongst Christians and Jews with great results and they're easy to use and adapt into various contexts, so they represent a valuable entry point for newbies from conventional religious background. I've never even heard of anyone getting backlash from praying them, including in preparation of doing something that would be considered extremely sinful (summoning a demon to get the operator laid, or even killing a person) or after such operations.