So, apparently the Association of American Colleges and Universities has been piloting the use of rubric assessments of "cross-cutting skills." They call their rubrics Valid Assessment of Learning in Undergraduate Education or VALUE.
According to Katrina Schwartz's reporting on the pilot last month, the professors involved were surprised by what they, themselves, learned by doing assessments in this way:
Professors began realizing how much the language of their assignment prompts communicated what they expected from students. That might seem obvious, but without other samples to compare to, professors just thought their students didn’t have the skills.
You don't get this type of reflection from multiple-choice tests.