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.
For it is a curious fact that though human beings have such imperfect means of communication, that they can only say 'good to eat' when they mean 'beautiful' and the other way about, they will yet endure ridicule and misunderstanding rather than keep any experience to themselves.