Annoying classes are a fact of life for a student. Whether it be chemistry with three hundred of your closest acquaintances, a professor with an absurd and unhealthy attachment to a particular way of formatting papers or the worst of them all: a department-wide class, with every section working off the same forced schedule.  
This can either go really well or really terribly, depending on which section and professor you end up with.
But why do these classes exist? Do some departments not trust certain instructors to make their own class schedules functional? Are they concerned about favoritism? Do these departments just not have enough instructors to manage individually?
Regardless of why, it is a mistake. If someone passes the checks necessary to get in front of a class and teach, they should be trusted to cover the material necessary in the given time while still adjusting to the needs of the class.  
With the strict structure of a multi-class schedule, some people are going to get left behind due to a lack of time to ask questions, especially as the class progresses and answers to these questions become more and more complex. Office hours exist, yes, and most professors agree they should be used more — or at least mine do — but there is zero chance that talking things over dozens of times in office hours is any more efficient than making a minute adjustment to the class schedule to allow for more time in lectures. 
So: just get rid of it. Toss that entire baby out with the bathwater of excessive gen-ed requirements. Just get rid of the structure entirely. Let the instructors and professors mix things up as necessary to ensure each section gets a proper grasp on the material. 
Let instructors make the tests for their sections individually, or at the very least, consult with the other instructors. Learning is not one-size-fits-all, and we pay for these classes. Why should the material be chained to the judgment of someone who is working with an entire other group of students?
Just get rid of it.