If the programs are spun-off, one thing is certain: budget allocations for frequent flyer program consultants will come by easier (and more often).
I don't think the downside of a spin-off exceeds the upside; however, requests for "yield management" to free up seats may end up being a more haggled and harried process. As Efrem said above, it's about how it works and not necessarily about ownership of the equity.