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That being said, most pure psyker builds will end up wanting Willpower anyway, since you end up with like 3 different disciplines, meaning eventually you'll end up wanting to use psychic assault, divination buffs or iron arms.
For your specific build where I assume you're mostly just giving all your AP away to Argenta, another stat like agility or strength for more defence might've been better though.
Then there's Sanctic Psyker which is its own beast.
A unique Psyker School that's based off Psy Rating and Resolve. Meaning it's the friendliest least characteristic dependent Psyker or even Origin in the game. All you need to do is increase Psy Rating and Resolve which it allows you to do by itself (Psy Levels, Psalms of Heroes, Word of the Emperor) and can be done with other abilities/talents, without even needing Fellowship investment (but of course, benefits from such as that increases Resolve).
It also scales and gets better as a fight gets more protracted, sort of representing the eternal struggle/resolve of the Emperor channelled through the character. That said there was probably room somewhere for Willpower here in order to make this school not so anti MAD.
General Psyker Talents:
● Still Mind - boosts resolve by WP bonus / 2 (Note that with this even Sanctic Psyker benefits from increased WP.)
Biomancer Psyker Abilities and Talents:
● Invigorate - restores (2 x PR + WP bonus) wounds
● Regeneration - recover (PR + (WP bonus / 2)) wounds each turn
● Pulse of Life - heals gain (5 + 2 x WP bonus)% crit chance
Diviner Psyker Abilities:
● Foreboding - Target's dodge cannot be less than psyker's (PER bonus + WP bonus)%
Pyromancer Psyker Abilities:
● Ignite - damage range of (1 + 5 x PR)-to-(WP bonus + 5 x PR) and warp burn of (WP bonus + 2 x PR) per turn
● Firestorm - inflicts Ignite (so WP impact is the same)
● Orchestrate Flames - prevents warp burn from ending, the damage of which is influenced by WP bonus
● Molten Beam - deals double Ignite damage and inflicts warp burn as Ignite (so also impacted by WP)
● Incinerate - deals double Ignite damage (so also impacted by WP) and bonus damage based on burn effects in play (including warp burn, so impacted by WP in cases where anyone is currently warp burning)
Telepath Psyker Abilities:
● Psychic Shriek - damage range of ( 1 + WP bonus x PR)-to-(4 + WP bonus x (1 + PR))
● Psychic Assault - deals Psychic Shriek damage (so WP impact is the same)
● Mind Bond - targets can use Psyker's WP to make willpower tests if it is higher
It is certainly possible to make a Psyker whose abilities and talents gain nothing from WP (Sanctic without Still Mind is the simplest example, but there are others). It is also possible to make a Psyker whose WP has some impact on their effectiveness without it being critical to their success (Diviner with Foreboding is an easy example).
However, I think that most Psyker builds are going to have medium-to-heavy impact of WP on their effectiveness, and are going to feel pressure to boost WP to gain the corresponding benefit. Pyromancer (except for builds using Pyromancer for talents and not using it for damage) and damage-focused Telepaths are the strongest cases for this. The impact on healer Biomancer is pronounced; I suppose you could skip WP but that will limit your heals greatly. Even Sanctic psyker should probably take Still Mind and boost WP unless your build absolutely cannot afford to boost WP.