At the same time this advice from http://stackoverflow.com/questions/42179012/how-to-shuffle-array-in-postgresql-9-6-and-also-lower-versions works, don't know why though:
words=> select array_agg(u order by random()) words-> from unnest(array['a','b','c','d','e','f']) u; array_agg --------------- {d,a,f,c,b,e}