Is it bad to not test the capability of the explainability of the student at the graduate level?
It depends on what you want students to learn.  Use open ended questions for learning critical thinking.  Either approach is good if you want students to learn facts.

Nearly always, at the graduate level, you want students learn "critical thinking" from the analyze/evaluate/create parts of the Bloom Taxonomy of learning.  Frequently this is the case at the lower levels of education as well.

Open-ended questions are necessary to demonstrate the ability to create, and can make it easier to tell if students are analyzing and evaluating.

If your goal is for students to remember a list of facts, then multiple choice questions are an efficient (but not necessarily better) way to test that.

"Understand" or "Apply" are often best addressed with open-ended questions, but could be addressed either way.