> their mental model is all wrong.

Is it? In Postgres, all FK references must be to a column with a PK or unique constraint or part of another index. Additionally, Postgres and Maria (maybe all SQL?) automatically create indexes for PKs and unique constraints. There's a high likelihood that a foreign key is already indexed _in the other table_.

Generally, I agree with your statement. Adding a FK won't magically improve performance or create useful indices. But, the presence of a FK or refactoring to support a FK does (tangentially) point back to that index.