Only War psykers suffer slightly from a lack of advanced specialties, alongside Commissars and Storm Troopers. Probably the least affected out of the three, but it's there.

weird utility

Look to minor manifestations listed under your psychic discipline(s). They're almost never going to be powerful compared to what a full power will do, but they're cheap, impossible to phenomena your way into a new character, and still do interesting things. Pyromancy's mass smothering of small fires, Divination's minor ability to find trivial/temporarily useful items or trip up a target, Telepathy's distractions or intuit thoughts - all might crop up in a game.