All students are unique and learn in different ways. One of the challenges of being a teacher is to learn how to reach students that learn and communicate differently and get a positive outcome for all or most of them. Standardizing a curriculum would take too much control away from the teacher and would not allow them to make the necessary modifications to make sure their students really learn, lowering the overall quality of education.
No, U.S. education should not be standardized because allowing input at the local level results in more choice. A local school district might have unique needs and demographics, and trying to conform to a rigid set of requirements does not allow for flexibility. Also, a local community might have unique values, and they should be allowed to reflect those values in their education system.