I’ve never been clear if the “progression” requirements were to be admitted to the department or to stay in the department, since my UW kid was Humanities. Most of his friends were Engineering, and plenty of them had to adjust their goals from Chem E or another “most demanding” major to something else because the gpa requirements were tough. So when you did meet a Chem E or major in some of the other “super elite” departments, you knew those were seriously smart cookies.
UW publishes its semester grade reports, course by course, department by department. A search for “grade distribution report” on the UW website will pull up Chem E and College of Engineering gpas.