Yes, dividing US history into sections would allow for greater depth when teaching. If one takes on such a large subject all at once, with no smaller categories, they are unable to cover all the relevant information. Even in a whole semester of classes, not all of US history can appropriately be taught. The span of information is too large and requires division into separate categories.
No, the teaching of US History should not be divided into separate categories, because we need to understand our history as a whole. We cannot understand the civil rights era if we do not understand slavery. We cannot understand current Supreme Court issues without studying the constitution and the intent of the founders.
I believe US history can be very specific but there is no reason to separate it into different categories until college. I believe his is important but public schools and high school students often have a hard time covering the information that is expected. Creating more history classes is more than likely not going to be viable at the high school level.
I do think the teaching of US history should be divided into separate categories. I think the categories should give the perspective of all people, too. Not just European settlers. It should also be divided by time and rule. Something that should also be included is the history of Native Americans.