In Chinese, usage of 四字熟語 a lot usually demonstrates sophistication and things like political announcements etc that want to sounds powerful and sophisticated use a big load of them. What does using them convey in Japanese? They seem a lot less common. Are they considered "clichés" as English expressions such that "it is raining buckets" or "... is in hot water"? Chinese seems peculiar for treating unoriginal clichés (used appropriately of course) as good style; did this carry over into Japanese?
I think apt use of 四字熟語 does demonstrate sophistication, just like, it seems, in Chinese. 四字熟語 are taught at the 高校 level, with other parts of the curriculum being 漢文, literature, etc., which alone should tell you something about the perceived status of these "idioms".
The infamous 四字熟語 exam question is:
with the correct answer being 弱肉強食, not 焼肉定食.
In serious writing, 四字熟語 are analogous to the poignant use of idioms, which one finds in well-written newspapers, for example. Maybe less like "raining buckets" but more like "skate on thin ice"...