The United States men’s national team will not count on its most high-profile figure for this summer’s Concacaf Gold Cup. Christian Pulisic, the forward from AC Milan, requested to be left out of the squad in order to rest after a demanding season in Europe.

Coming off a disastrous showing in March’s Concacaf Nations League finals, with a fourth-place finish following defeats to Panama and Canada, this latest development is a significant blow for the U.S...