"Is it pernicious to claim that learning can be measured? "
No, the pernicious part is the claim that the teacher is incapable of making the assessment and deferring all assessments to some bureaucratic body, with no input from teachers, that decides what to measure and how to measure it.
Teachers have always assessed student progress. It's part of how they decide how to pace the class, what to teach, what to practice, etc.
Joanna