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
The Enterprise is always the only ship that’s within range to mitigate a crisis, even when it is near Earth, the capitol world of the Federation and where the big orbital shipyards are.