I think you could get away with it under the right conditions.
Like, during Infinite Crisis when the villains were starting to organize, I could see Superman deciding to go after the lower rung of villains. A show of force in that situation would have been warranted as it would be both a proactive attempt to weaken the Secret Society's ranks and a spectacle to remind people that Superman and the other heroes can still stand tall. It'd be part intimidation tactic and part pro-hero rally.
If Clark just wakes up on a random Tuesday and says "You know, I think I'll clean out the Fearsome Five during my lunch break" it might not work. As Pak used to say, Superman doesnt punch down.