Why can I edit search_path but can't reset it?

Question

PostgreSQL

I connect as superuser and easily add the search prefix with this command:
ALTER ROLE dship SET search_path = "$user";

But I can't reset this field like this:
ALTER ROLE dship RESET search_path;
Not even like this:

ALTER ROLE dship in DATABASE dship RESET search_path;

The command works without errors, but show search_path; returns the previous value: "$user", public

What am I doing wrong?