1000ft separation isn't much when you have an issue, if you loose an engine at cruise altitude you typically cannot maintain that altitude for example.

Oceanic procedure, without radar control, is to turn 45 degrees off track while descending, but it takes a little bit of time to set all that in motion when things go wrong while you were just seconds before happily cruising straight ahead on autopilot (autopilot is mandatory above 29,000 ft in a lot of airspace)