You have a point, but on most routes competition would probably kill the route, especially if two carriers made the decision to pull their routes as unprofitable at he same time. The debacle of UA and AA both serving the New York area, and back in the day when Wardair and Air Canada both served Toronto (those were the days!!!) when AC saw off Wardair and promptly closed the route down themselves.
BHX got their fingers very badly burned when British Airways pulled out of BHX, having been supported, at morally for decades and that certainly supports your argument for competition.
In reality it's probably a no win situation for airports of BHX size and smaller. The principal London airports and Manchester probably don't suffer the same dilemmas.