Skipping grades and other forms of "meritocracy were almost brought to an end by Progressive Education that started in the late 19th century, and picked up steam in the 1920s. As late as the publication of Herman Wouk's "City Boy" (1928), it was commonplace, but fell out of favor shortly thereafter. In the early 1890s, an 11 year old immigrant, Mary Antin, was forced to start school in the first grade, but "skipped" to the sixth grade in one year. This would not happen nowadays.
"Traditional" education, which held sway in the 19th century in America, was a carrot and stick affair. ( won't go into the 18th century since there was no "USA" for most of the century. A student either knew things associated with a certain grade level, or s/he didn't. If not, the student was "held back." If "advanced" for their age, students were pushed forward into groups with older people. That meant that in any given grade, there could be people of several age levels. Prior to the beginning of the 20th century, before "universal" education, children would start school at different ages, and by that fact alone would reach a given grade at different ages, so no one thought anything of it then.
The theme of the "progressive" education was that the purpose of education was to help students progress in life, not in school, so that schooling was the means to an end, not an end of itself. This coincided in America with "universal" education. For a "life" educational project, it helps to have students of roughly the same age and experience, not academic ability. That meant that classes would be homogeneous by age, and heterogeneous by educational accomplishment (the reverse of traditional education). But the "progressive" educators had an answer for that; teachers were supposed to treat students as individuals and teach them at the "own" levels, not as members of a class. That's possible when you have small class sizes, typically no more than 25-30. The teacher's other function, equally important to education, was to conduct "group" activities.
So skipping grades went out of fashion when the idea of sorting students by age replaced the idea of sorting them by academic achievement. It became somewhat popular during and shortly after World War II, when society placed a premium on "efficiency" (even at the collegiate level, George Bush Sr. completed a four year program at Yale in two and half years). But "progressive" education regained its hold by the 1950s.
Additional source: Hyman Rickover, "American Education: A National Failure."