Another reason why arithmetic intensity is a useful heuristic for finding a better algorithm -- not only is arithmetic generally easier to parallelize, but it is less costly in terms of energy, so even if we rearrange an algorithm in such a way that we have a lot more arithmetic instructions for the sake of eliminating a few memory instructions, this is not Goodhart's Law at work, because arithmetic intensity is still a useful metric.
Another reason why arithmetic intensity is a useful heuristic for finding a better algorithm -- not only is arithmetic generally easier to parallelize, but it is less costly in terms of energy, so even if we rearrange an algorithm in such a way that we have a lot more arithmetic instructions for the sake of eliminating a few memory instructions, this is not Goodhart's Law at work, because arithmetic intensity is still a useful metric.