First, a political scoring system that rewards ordnance and ignores outcomes makes violence cheap and diplomacy expensive. Fifty-nine Tomahawks buy a week of admiring coverage. Removing most of an arsenal of mass destruction buys a decade or more of sneering. Presidents can do that math, even Trump.
Second, allies also learn the currency of force and denominate their demands in it. The Gulf states were not grieving over American reliability regarding Iran in the autumn of 2013. They wanted the United States to eliminate their Assad problem, and the threat of chemical weapons gave them their best lever for the job. Obama’s deal did not destroy their faith in American protection—it frankly told them nothing about what the United States would do to protect them if, say, they were attacked by Iran. What it did instead was take the lever of chemical weapons away as a reason for a forceful U.S. intervention in the Syrian civil war.