Air power can either paralyze the enemy's military action or compel him to devote to the defense of his bases and communications a share of his straitened resources far greater that what we need in the attack.
I think it's very important to remember that so much of the work that gets done between countries is not done at the level of presidents, but is done within various agencies, whether it's law enforcement or economic ministries. And when they establish relationships and systems of communications and shared projects and shared visions, those structures continue even after any particular president is gone. It builds trust and understanding between countries that are critically important.