For me, from the UK, jaywalking is a strange law, we’ve never had it and I don’t really know why it exists elsewhere. It makes streets more pedestrian friendly and encourages drivers to look out for them.
Moved from Auckland (with fairly weak, unenforced jaywalking laws) to London and I've found that jaywalking is essentially required here due to how slow most pedestrian lights tend to be. Perhaps in places with stronger jaywalking laws, lights are timed in such a way that you don't have to wait too long to cross legally?
There is no such thing as illegally crossing a road in the UK. Green light, red light, no light; it doesn't matter, they're just advisory. You have the perfect right to cross whenever and wherever you feel like it. If it causes an accident I believe you can be liable, but ultimately it's just common sense and your own self-preservation instinct that governs your behaviour, not the law. I believe the only exception is on a motorway.