That is seriously the wrong reason to add cmpOpts=>{mathQuillOpts => "disabled"} to a problem. That option is certainly not intended for that. The option is intended for problem answers for which a MathQuill input does not make sense such as a purely textual answer.
For the purpose you are describing you should disable MathQuill for the course.
You should also note that students can disable the toolbar. On a touch screen touch and hold any MathQuill input, and a menu will pop up that has the single "Disable Toolbar" option. It can be re-enabled again in the same way. I would prefer that you teach the students this, rather than disabling MathQuill and certainly do not add that option to the problem.