They could instead send the list of hashes to the device (which they already must trust is faithfully computing the local hash) and just let the device report when there are hits. It would be much more CPU and bandwidth efficient, too.
The PSI serves the purpose that if Apple starts sending out hashes for popular lawful images connected to particular religions, ethnicity, or political ideologies that it is information theoretically impossible for anyone to detect the abuse. It also makes it impossible to tell if different users are being tested against different lists, e.g. if Thai users were being tested against political cartoons that insult the king.