https://www.theatlantic.com/health/archive/2013/07/the-vitam...
The placebo effect is powerful.
I highly recommend reading Topol's "The Creative Destruction of Medicine" for more information.
See gwern on vitamin D[0], which shows it's likely not a placebo, (n=1, of course, but coincides with a lot of not-quite-as-well-executed self experiments from other people)
Iron and/or vitamin B3 (Niacin) make a huge difference for RLS[1]; You'll find some peer reviewed reference for iron, mostly anecdotal for B3 (some better executed than others).
As a general rule, if you eat a variety of foods, some of which are grown naturally and not processed to death, and have decent exposure to the sun, then - no, you don't need vitamins. But among my peers it seems that this rather simple set of requirements is often not satisfied, and vitamin supplements are needed (usually B12, D, and Iron deficits are found for whoever does testing).
It's well proven that Folate during pregnancy significantly reduces the incidents or neural-tube defects.
It's well proven that putting some B vitamins back in the flour after it's milled significantly reduces psychiatric presentations.
Sounds like you've made your mind up though.