It used to be a staple of old b/w sci-fi like Flash Gordon. Though really crappy special effects (sparklers on model rockets woohoo) never made it quite as exciting and they often got the timing horribly off. And I think it was in like 5 or 6 episodes of the silverhawks TV show. Plus there's the airplane versions that aren't sci-fi but have the escape from exploding hangars, blimps, etc. And then the boats getting out of blowing up buildings (James Bond did this a few times).
Really it's a very common thing.
Well, destroying something important and then getting out in the nick of time is very old, yes. But given that this is a very large spaceship, that earlier in the mission we have to do a trench run, and how often STO has ripped off Star Wars, yeah, pretty sure that's all the devs were thinking of, IMHO.