When do you use superscript affiliations and when not?
If many authors share the exact same affiliation, use the superscript form.
If one or more authors each have multiple affiliations, use the superscript form.
If authors come from departments whose names indicate distinct disciplines, and these multiple expertises are relevant for the multidisciplinary aspects of the paper, do not use the superscript form.
Use these rules as rules of thumb, not as ironclad rules. In the end, this is a matter of personal style and opinion.