Thanks everyone for your replies. How disappointing that extra luggage is not an alliance-wide benefit. I do most of my travels on RTWs which normally involve more than one carrier. It is a huge benefit to have the extra luggage allowance apply across the network.
Number_6 you are right - I did an AA Plat Challenge when I had to fly LAN (only option) earlier this year. Thought I might as well get it. Unfortunately it looks like I won't be able to make use of it as I generally have around 30-40kgs with me (presentation materials). I'll email CX and ask them if they would give me 30kgs if I choose them for my upcoming flight to Japan. If they don't it'll be SQ or NZ.
Just out of curiosity. *G gives F pax 60kgs plus 2x7Kgs handluggage- how much would you get on CX? Of course itineraries through the US get 3pcs of 32 kgs plus 2 pcs of handluggage at 7kgs each, so a total of 110kgs. It would be great if this were actually topped by some other airline.