General Westmoreland was, of course, the commander of US troops in Vietnam. As such, he was responsible for the conduct of the entire war. This meant that he had to think very much in a strategic way, conducting the war in such a way that would help achieve the goals that the civilian government of the US wanted to achieve.
Because of this, Westmoreland had to set out fairly restrictive rules of engagement. He knew that the US needed to look like the "good guys" in this war. That meant limiting civilian casualties and it meant trying to prevent the US from looking like it was waging an excessively aggressive war. These needs made it so that Westmoreland had to issue rules of engagement that would make life more difficult and more dangerous for the soldiers who actually had to do the fighting.