The good news is that Campbell’s Law does not mean we should give up on assessing students and holding school systems accountable for their academic success. Research shows that certain kinds of exams—those that require essay writing on broad themes, for example—enhance student learning of key concepts. We can also assess students by requiring them to give oral presentations, or by looking for growth in portfolios of their work over the course of a year. Effective teachers produce students who excel when held to these more sophisticated standards, which are difficult to fudge or cheat.
This actually matches my experience with teaching quote well. Standardized tests are the only feasible way to handle large classes (how else do you assess 400 students?). But my best results come from asking essay questions (in free hand) and requiring many, many class presentations. Not only is the assessment a lot more complete but I gain a very good idea of what concepts and ideas that I failed to communicate well.
This type of assessment is a valuable tool in making next years class better than the one before it (a process I hope never stops). Sadly, it is not well suited for mass comparisons between schools. But then complex phenomena rarely summarize well (just consider confounding by indication for how hard it is to use summarized data to capture complex processes).