You test at least moderately close to the actual target and you punish those who are breaking the rules brutally (it is actually food safety!). Instead we allow Olive oil that isn't and Fish that aren't because, nobody has died yet? Allergies are possible even at very low levels.
My real point wasn't the simplicity or cheapness, but often the biproduct of those is that it's a test you already have that doesn't measure what you want (nitrogen rather than protein). In the case of Olive oil, if what we cared about was it's fluoresced color rather than the material in it, that would be great.
If what we care about is components, random GC/IR spectroscopy (perhaps after centrifuging) to see the actual compounds with consequences would be a better choice than the cheapest thing they can just add another weird chemical to defeat.