Perhaps it is each airlines particular systems or operations that requires the torn tickets. Virgin America's tickets don't come with any part to tear. At boarding, they scan it in and hand it back to you. That would work for a wallet size as well. For people printing a pass, well, they're using a full sheet of paper anyways, so there could be a different design for printed tickets, the same way printed concert ticket designs are different than official tickets that are mailed to you.

Also want to note that I missed the part about the thermal printing, which would nullify the ink cost issue.