as others have said there is perhaps some confusion, and one of the benefits offered to frequent flyers of a particular airline that is also part of an alliance (like OneWorld in this case) is that the flyer can earn miles and point across the alliance (with some exceptions) using the one FF program is part of, like for what you are saying, using the BA FF number with Cathay Pacific flights (or AA, Qatar, Iberia, etc). You do not need to register with the each airline FF programme as you can simply book as guest on each airline website, and enter your BAEC number in the appropriate section of the booking (FF).

There are instances, particularly across the airlines also sharing the loyalty/miles currency, like AirLingus, BA, Iberia, Qatar and soon Finnair with Avios, that you may want to register when particular promotions happens /have sign up bonuses and/or also offer ways to earn more Avios from third parties, that can then be inter-transferred across FF schemes.