The main reason why reformers wanted to spread uniform cultural values was so that America could be a homogeneous and democratic society.
Educational reformers like Horace Mann wanted to create a a more egalitarian society. They felt that a society where more people had the same values and the same education would be more democratic because the people would be more like one another.
In addition, some reformers wanted to create a society in which people would be well-suited to work in the new industrialized economy. They needed people to be more conformist so that they would fit in to the needs of a society where people worked for and with other people outside their families.