If you will hold only a bachelors degree your statement can be quite general, aligning with the department in general - even quite loosely. If you will hold a masters it should be somewhat, at least, more specific and perhaps related to the research of some group (more than one person) of faculty.
The first task in most US doctoral programs is to pass comprehensive exams, not immediately begin research. There is time for reflection and refinement. You will eventually need to align your dissertation research with those of an advisor, but that isn't normally the first task.
Caveat: There are a few exceptions in the US, especially when your funding is initially coming from some specific research group's funding under a specific PI. In that case, you need to think about that and about how your ideas fit with theirs. But even then, for a bachelors holder there is a long road ahead with many options.