My favourite is still from the first episode of the 90s Superman animated series, where Clark initially tries to catch the falling plane by its tail... which snaps off in his hands because physics doesn't work that way.
I think it'd be boring if a hero could use their powers perfectly right off the bat and not have any unforseen consequences (though I also don't keep up with a lot of superhero stuff, so not familiar with those scenes)
Overseas, Kamen Rider Gaim did something similar after Kouta(the main character) got his transformation belt. He tried to do a whole bunch of mundane things with it cause he thought it'd make him better at them and they all go horribly wrong.
Arrow didn't have one (though Oliver got hurt a lot in flashbacks), Supergirl already had her powers, LoT gang also already had their powers mostly and in Black Lightning discovering your powers seems to be more associated with emotional trauma than anything comedic