How to phrase questions about spotting design issues in programs
It is true that these issues can be problematic in some cases, however, this depends on the context and the usage of the class.


The "design problem" that you were hoping they would find also depends on the context and usage of the class. We have no idea whether the users of this class are obeying your JavaDoc. In fact, I could see an argument that your "design problem" is invalid because anybody who violates the JavaDoc is going outside the bounds of your design in the first place! Compare that to the functions with no JavaDoc, and honestly I'm more convinced by your students' answers than I am of your intended answer.

Asking "what is wrong with the design of this class" is too broad. You need to provide more context: perhaps provide the UserSystem class and then another class that uses it incorrectly (by creating a new UserSystem instance for every user, for example), and then ask what the design problem is in that code and how it could be prevented in the future.

If you want a specific answer, you need to ask a specific question. All of the answers your students provided sound perfectly reasonable to me.