Now I'm surprised that a set-returning function is even allowed in SELECT clause where the values have to be scalar.
AFAIK the lateral construct, which is required to avoid doing just this, is a relatively recent invention for SQL. I infer from that fact that the ability to execute a set-returning function in the select clause has always been allowed. When done, it behaves in a manner similar to an inner join against the single input evaluation rows (i.e., the one where, typically, the argument values come from). An inner join of one row and zero rows is zero rows which is the behavior you are observing.
A true scalar subquery does not have this limitation - even when correlated it gets joined to the parent relation in a left join manner and so the single row in the parent relation will always remain and a zero record outcome will result in null for the scalar subquery output.
FWIW this is the same behavioral dynamic that happens for Regular Expressions. Our original regexp_matches() function eventually was supplemented with a regexp_match() function to (mainly) allow for prettier queries. I like having the option to choose the desired function instead of having to write the normal single-result case always using a scalar subquery.
Also how come a set contains two elements with the same value?
That is just how SQL works. A result set does not have all of the characteristics of a formal mathematical set. Every produced row has a unique identity independent of the value(s) of the fields. There are SQL operations that can remove all but one of these identities from a result set based upon the comparison of the field values (DISTINCT, UNION, etc...).
