What are some technical reasons for not including N-ary multiplication in the SQL standard?
Yes, the PostgreSQL core team has spent days deciding that this should not be included in core.

Seriously:


a mul operator is not in the SQL standard. 
With PostgreSQL's extensibility, it is trivial to define such an aggregate function yourself:

CREATE AGGREGATE mul(integer) (
   SFUNC = int4mul,
   STYPE = integer,
   INITCOND = '1'
);