An airline wants a codeshare principally to pretend it serves somewhere and therefore provide local feed for a larger route, or to deepen a commercial exchange on specific routes with a partner airline where revenue is being shared to some degree between the parties.

For instance, intra-Asia (I assume you mean, shorthaul on CX ex-HKG) makes sense because AA recently started serving HKG. By codesharing onto local CX flights, AA can draw feed to connect to its new HKG service. CX will have to decide carefully if it wants to cannibalize its own prime services to the USA, but if the price is right, then maybe that's better than AA working more closely with JL. AA also has an arrangement with JL as well.

Looking at another one you mentioned, MAD-DOH, well AA doesn't serve DOH itself, but QR is a major oneworld partner. There might be good reasons to cultivate that relationship, even though AA already has a partnership with EY.

And then you have BA and AA codesharing everywhere on their transatlantic and domestic and intra-European sectors, together with their partners AY and IB. That's part of their "joint venture".

However, on CX FCO-HKG, there is really no reason for AA to codeshare on that at all. It doesn't give either CX or AA any advantage. It doesn't feed any real AA sectors. I doubt AA would want to buy a block of space or subsidise space on that flight.

Also, there are legal and regulatory restrictions on codeshares; often regulators have to be consulted; maybe domestic codeshares can only exist when part of a fare component with an international prime segment (as in the USA), maybe a codeshare is only allowed if it connects within 24 hours to a prime flight (such as in HK). Although these technical restrictions are often not enforced on oneworld explorer tickets!

What I was also going to say, is even if AA doesn't have a codeshare, you might earn more miles (I don't know the details) if you pick a "closer" AA partner, for instance use the BA codeshare instead of the S7 prime flight. Not entirely sure about AA's programme, but it might be worth thinking about.