I don't think a president has any obligation to honor commitments started by other presidents unless there is a written contract that is approved by congress and signed by the president, in which case honoring that contract serves the American people by valuing our word.
International contexts change, and any good president needs to react and execute in that context. I'm not incredibly versed in this situation, to be honest, but I don't think it's reasonable to say that any President has to be consistent with the actions of previous presidents if/when it doesn't serve the American interest.
It's a good thing that you are not president. Even in contract law, verbal contracts are (except in special instances, e.g. real estate) are just as binding as written contracts. The problem with them is that they are less enforceable because they are much harder to prove.
Other nations expect that president will honor the commitments made by their predecessors. If presidents did not do that, America's committment would not be trusted, and that would certainly do harm to American interests throughout the world. Imagine if a president were to say to another nation, "well, maybe my predecessor said that, but you can't prove it. It isn't in writing. So forget it"). There has to be continuity in foreign policy.