Function executes faster without STRICT modifier?

Maybe an overhead from the repeated function call that is streamlined away by inlining the function?

That's what I'd guess. You've got a very simple expression there. An actual function-call presumably involves stack setup, passing parameters etc.

The test below gives run-times of 5ms for inlined and 50ms for strict.

BEGIN;

CREATE SCHEMA f;

SET search_path = f;

CREATE FUNCTION f1(int) RETURNS int AS $$SELECT 1$$ LANGUAGE SQL;
CREATE FUNCTION f2(int) RETURNS int AS $$SELECT 1$$ LANGUAGE SQL STRICT;

\timing on
SELECT sum(f1(i)) FROM generate_series(1,10000) i;
SELECT sum(f2(i)) FROM generate_series(1,10000) i;
\timing off

ROLLBACK;