I don't think it's so much the exclusivity but that if you are a loyal CX customer saving to Asia Miles at its relatively low earn rates, it takes more points to redeem seats on CX with more restrictive rules than those who earned AA and AS miles much more easily. So it feels like the airline biting the hand that feeds them.
That's precisely the reason why it is more expensive to redeem Cathay Pacific through Asia Miles. There are too many people loyal to Asia Miles and too many Asia Miles floating around. In another way, Cathay has no competition in HK.
On the other hand, AS is small in US and not many people from AS redeem Cathay Pacific.