This is a pretty bogus criticism. Sure, random assignment is necessary to establish a causal relationship between the factors you are comparing because otherwise there may be some confounding variable. But t all depends on what they are doing with these measures–what inferences are they trying to make. I would think we are most interested in having teachers do the things that work best for the students in their classroom, and not for a hypothetical randomly-chosen student who may have different needs. If for most kids, making them eat peanut butter helped them do math better, a teacher in a class with nut allergies might be expected to try other things.
The inferences we want to make might really be to only the sample space of the particular students in their class taking tests, or maybe to all the classes this teacher might teach with all the students who might take his/her class over his/her career. As such, measurement can help us know whether something the teacher did was better than what they did last time around. The entire field of epidemiology is essentially based on inference done from quasi-experiments that do not allow for random assignment, and it has saved countless lives.
