After a dangerously long fast, the first thing they recommend doing is getting micronutrients prior to eating: "All guidelines recommend that vitamin supplementation should be started immediately, before and for the first 10 days of refeeding". So obviously if those vitamins weren't skipped in the first place, it would be less dangerous. Along those lines, another study indicates that something like a multivitamin is probably as effective during a fast as it is after eating: "Iron absorption values obtained when the supplements were administered to fasting women were not significantly different from those obtained after postprandial administration". Several studies also show that taking a multivitamin acutely improves cognitive function, the most relevant one being that "MVM supplementation appears to potentially offer an effective intervention in the dietary restriction regimen to combat daily life physical and mental stress". In general it was determined that "there was no clear decrease or increase in mortality from all causes, cardiovascular diseases, or cancer among multivitamin supplement users", yet food is fortified because vitamin deficiencies occur, so basically it couldn't hurt to take a vitamin, or it would most likely help prevent the complications associated with fasting or energy restriction, which is mostly about macronutrient restriction, and its benefits don't seem to be related to micronutrient restriction.
In other words, I don't see any evidence in favor of fasting to limit micronutrients. There seems to be more evidence that they shouldn't be limited, unless it's a specific medical intervention. Besides, most people don't do absolute fasts intermittently, they at least drink water, and should probably at least take a vitamin too, or sometimes electrolytes (for thermoregulation and extended fasts). Intermittent vitamin-mineral supplementation has been shown to be effective also (which would be well timed during a "health fast" then). This could be referred to as a form of "fasting mimickry" too, although that diet usually gets into incorporating some macronutrients, for the sake of eating with an end result similar to fasting. Well, I'm not looking for an excuse to eat during a fast, but fasting has its limitations anyway (you know, it is in itself a limitation, or a question of what you want to limit).
- Refeeding syndrome: what it is, and how to prevent and treat it
- Effect of food on the availability of iron from three multivitamin/mineral supplements during pregnancy
- Effect of chronic unpredictable stress on short term dietary restriction and its modulation by multivitamin-mineral supplementation
- Multivitamin Use and the Risk of Mortality and Cancer Incidence
- Multivitamins and minerals modulate whole-body energy metabolism and cerebral blood-flow during cognitive task performance
- Acute Effects of Different Multivitamin Mineral Preparations on Mood, Cognitive Performance and Functional Brain Activation
- A periodic diet that mimics fasting promotes multi-system regeneration, enhanced cognitive performance and healthspan
- Relationships between micronutrient losses in sweat and blood pressure among heat-exposed steelworkers