It is conceivable that an airline might be interested in purchasing Metro or to be part of a syndicate bidding on the airport. An airline might stand to benefit by being the owner of the entity to whom it is paying rent and landing fees.
It is probably not in the best interest of the success of Metro to allow this to occur. The airport owner's best interest (whether publicly or privately owned) is to have many airlines using it. If an airline were to become an owner, the airline might be in a position to drive out other airlines, thus creating a monopoly for itself in the Detroit area.
However, it would probably also not be in the best interest of an airline to become an airport owner. An airport that was not competitive would lose money and therefore become a liability on the airline's balance sheet.