I wish they would. I know CO Onepass members earn EQM's when they fly AS. If AS members could earn EQM's on CO, AS and CO are the only airlines I would ever fly.
To give an example: I'm going to Houston next week. CO has nonstop and direct service IAH-ANC. However, I elected to take AS through Seattle and connect onto CO there just so I could pick up EQM's on AS. If I could earn them on CO, I would have preferred to take their nonstop.
Then again, maybe that's why AS doesn't allow customers to earn EQM's on CO