I think Wraith meant having their sanctioned psykers look over suspected/accused psykers rather than over every baby. You still need to weed out the people accused due to superstition from the actual psykers, and in the interim between black ship arrivals having your own psykers look over candidates is the most convenient option. Given how minor some psychic manifestations are many psykers can be mistaken for people who're just unusually lucky or unlucky or have an unusual knack for bonding with animals.
So if John Smith gets hauled in for always rolling sixes in dice games and having a weird birthmark you need someone to tell if he's actually a psyker with that one minor power from DH which I have forgotten the name of or just a dice cheat with a birthmark.
EDIT: Ninja'd by Wraith.
It's also worth bringing up that some worlds never get visited by the black ships, they instead ship their psykers to more important planets that serve as hubs for resource gathering and distribution. It was a plot point in the Siege of Vraks FW stuff that Vraks held the collected psyker tithe of several planets who weren't important enough for a black ship to visit them.