Is there a lot of writing in PhD programs in top-rank US schools?
Yes, you should expect to do quite a bit of writing as part of your courses in any high-rank U.S. university.  It is, indeed, good practice, and in a good university your work should indeed receive significant scrutiny and feedback from the instructors.

Furthermore, I would not be so quick to dismiss such practice in technical writing.  First, the quality of prose that you have produced in the initial version of this question clearly indicates that you have a long way to go before you can routinely achieve a high professional standard of writing.  Second, no really good writer ever considers their art to be finished, and that includes long-experienced academics.

Do not forget that communicating your technical work effectively is just as important and difficult, if not often more so, than doing that technical work in the first place.  I know people who have run their careers into the ground from a reluctance to invest sufficiently in becoming comfortable with scientific writing.

In short: if you want to be a scientist, you've got to embrace the writing.