Your thinking has been confirmed by studies
(side note: an interesting theory of one reason why many women crave chocolate is because cocoa contains iron, and other minerals, and women tend to be low in iron).
And it's not even just micronutrients that drive excessive hunger -- protein, which is an essential macronutrient that many people don't get enough of, is shown in studies to drive calorie consumption until the protein needs are met. That's why protein foods tend to be very satiating.
As for supplements, there are many things to discuss, too many for this forum
But just a couple of comments:
1) Due to industrial agriculture, nowadays the soils are depleted of some nutrients so even someone with a great diet (which few people have anyway) will find it difficult to get enough of some essential nutrients. Also, some regions' soil and water have naturally lower levels of some nutrients. An example is iodine. Before iodine started being added to salt last century, there were widespread "goiter areas" where due to lack of iodine, people developed goiters (thyroid enlargement). Iodine deficiency is devastating and can lead to retardation in children, among other things. Nowadays people are eating less iodized salt (because fancy un-iodized salts have become popular, like pink salt) so iodine deficiency is increasing again.
Another example is magnesium, which is essential for a lot of body processes and which
research shows most people are deficient in, so supplementing magnesium would decrease their chronic disease risk. Magnesium deficiency is especially dangerous for cardiovascular disease risk. "
because of chronic diseases, medications, decreases in food crop magnesium contents, and the availability of refined and processed foods, the vast majority of people in modern societies are at risk for magnesium deficiency. Subclinical magnesium deficiency increases the risk of numerous types of cardiovascular disease, costs nations around the world an incalculable amount of healthcare costs and suffering, and should be considered a public health crisis. That an easy, cost-effective strategy exists to prevent and treat subclinical magnesium deficiency should provide an urgent call to action."
Side note: there is unfortunately a lot of ignorance in the medical community when it comes to supplements, or nutrition in general; one example is the fact that many doctors prescribe calcium supplements for bone health/osteoporosis, without realizing that magnesium is also needed for bone health and the extra calcium competes with magnesium absorption.
Another interesting example of a little known mineral is lithium which seems to be very important for mental health. Several studies showed that areas where water contains more lithium have lower suicide rates. Most people don't know whether they are deficient in lithium, and more and more evidence is showing that a small dose of lithium seems to benefit people with depression, anxiety, and ADHD.
Also, some nutrients are concentrated in foods we used to eat but don't anymore, such as liver and organs.
There are many more examples, point being that ideally of course we should get all these nutrients from food, but unfortunately in the modern world that's just wishful thinking for many if not most people.
2) The discussion above was about nutrients that everyone needs, i.e. vitamins and minerals (which in theory we could get from food alone in an ideal world, which is not really the case usually, as discussed above). But there's a whole other group of fascinating supplements which are highly concentrated/purified and that we generally can't get from food. Nootropics fall into this category: these are supplements that enhance mood and cognition/memory. They are used by both healthy people who want to enhance their mental/cognitive health and people with certain issues such as ADHD, for whom nootropics are a great alternative to drugs.
Another example in this category are plant extracts, such as adaptogens. These basically naturally enhance the body's response to stress (they're designed to be taken occasionally when going through stressful periods).
There are many other plant extracts that people have used for centuries for all kinds of health purposes (some people think of supplements as vitamins/minerals but e.g. an herbal tea is essentially also a kind of supplement).
I could go on but I'll stop here
(won't even go into vit D which the human diet is naturally poor in, so we have to get it from the sun, but at many US and Europe latitudes the sun isn't strong enough to produce vitamin D half the year so unless we stored up enough vit D by spending lots of time in the sun in the summer with minimal clothing, we must supplement vit D in the fall and winter. Plus older people are less efficient at making vit D from sunlight so they need to supplement even more.)
