I had similar issue too. AY issued ticket, on AY flight number, but operated by CX.
Called AY CC and they said they can't assign me the seat and I have to call CX.
Just called CX and they were able to do the seat assignment in few seconds.

Shouldn't operating carrier be always able to book the seats even though the ticket is sold by other carrier?

Maybe u should try HUACA?
Just tell ur AY PNR and ask to get the seat assignment.