I think you can have the master list but also allow teachers to create one or two custom assignment types. We all set up assignments differently and sometimes the master list does not fit what we categorize assignments as. 

I understand the need, but I think how you've described it would cause a lot of problems.  Chief among them is reporting.  If teachers are allowed to supply their own assignment types, who's to say that they don't create one called "essay" when "Essay" is already provided.  Additionally, if a teacher marked the assignment type as "major" it could create a lot of confusion in determining what students are actually overloaded or when a test or other major assignment could be assigned.

That being said, I could see how a "Custom Assignment Category" for teachers could be helpful.  For example, an assignment with the type of "Lab" could have a second option, which could be supplied by the teacher.  This should be a dropdown selection, but allow teachers to add their own options and be available for any courses the teacher taught.  This would avoid any potential issues with reporting, and give teachers that additional level of customization you're looking for.