Humans get enough arsenic from water and other background sources that deficiency is virtually unknown. My understanding is that there was historical anecdotal evidence for rare arsenic deficiency from animal husbandry that caused it to be investigated.

These days they systematically test for the trace micronutrient status of e.g. heavy metals by inducing extreme deficiency using mammal models. Most of the time nothing happens but it is difficult to eliminate the possibility of contamination creating a null signal.

Probably the most surprising element for which they have suggestive evidence of biological necessity is lead.