Some obvious examples
- the holodeck gets a fatal software error and people are stuck in a classic novel
- a shuttle breaks down and crashes into a habitable planet
- the federation loses a space battle, but thankfully there’s some space jungle (nebula, asteroid field, etc) to hide out in, thankfully within sub light distances
Every single time a pre-warp civilization is going through a major crisis, the officers need to have a meeting in the important meeting room to discuss whether or not intervening and breaking the prime directive would do more good than harm while also displaying the worst bits of moral cowardice while debating it.
Yes, I really hate PD episodes from TNG onwards. I know lower decks lampshaded the most egregious one in TNG, where Picard decided to take his ball and fuck off at the end.