it is not entirely clear why. My personal theory is that AS has individual agreements to CX JL, etc, before joining OW, so they have a different reimbursement rate. It was deemed too low/too much volume that both CX and JL restrict their awards to AS. CX completely shuts down premium cabin to AS about a year ago, while JL just releases 1 fewer seat to AS in J, and never in F. Given vast majority of time only 1 J is available anyway, AS sees significantly fewer dates available.
Some others like HU I think AS just never bothered to integrate properly.
And for JX I think AS also never came around to doing EQM properly.