The conventional wisdom certainly is that all-malt worts are deficient in zinc. It's in all the textbooks, etc. I'm sure it stands on solid scientific ground. It's the main reason why nutrient is recommended.
But what about the observation that plenty of beer has been made both commercially and at home where no nutrient/zinc was added, and the beer turned out fine, fermentations went smoothly and consistently, etc.? If there wasn't enough zinc, doesn't it logically follow, for example, that acetaldehyde would be tasted in the finished beer? Or other off-flavors?
For me, regardless of what the textbooks say, empirical evidence conclusively points to there being plenty of zinc in unfortified wort. Perhaps there is less of a surplus of zinc relative to other minerals/nutrients, hence the "wort is deficient in zinc" mantra. But my experience and that of many, many other brewers indicates that there's still more than enough zinc for a normal, healthy fermentation.
Can it hurt to add nutrient? The consensus seems to be probably not, as long as it's used sparingly. It should be kept in mind that too much zinc, and many other minerals, is bad for yeast. It doesn't take much to go from "enough" to "too much". So my approach is to stick with the naturally occurring levels of nutrients--except when I brew my American lager, which uses 30% rice. In this case, the wort probably is truly deficient in zinc.