"Most of what makes neighborhood streets dangerous is pedestrians" - not in the UK.
Let me restate that. Most of what makes neighborhood streets dangerous is vehicles and pedestrians using the same space at similar times.
Pedestrians have priority over all forms of transport on the road.
Who has priority is largely uninteresting, because ultimately if a car hits you, you're still probably dead whether you had the right of way or not.
Vehicles make the roads dangerous
Ostensibly, sure, if you got rid of all the cars, streets would be safer for pedestrians, but they would also be a huge waste of space, because pedestrians don't need huge roads to walk. Roads exist principally for cars. The fact that pedestrians have to cross them is just an unfortunate design constraint that's hard to avoid cheaply, and giving pedestrians priority is mostly just feel-good policymaking that doesn't solve any of the fundamental problems.
The only truly safe way to share the space is to ensure that pedestrians aren't in the road when cars are. The best approach, at least in cities, is second-floor walkways, so that pedestrians and cars are never vertically at the same traffic layer. A slightly less optimal, but still reasonable approach is to give pedestrians a separate walk cycle in which the entire intersection is theirs. Pedestrians have priority during that cycle, and cars have priority the rest of the time, and as long as everyone follows the rules, nobody gets hurt.
But none of those solutions work for neighborhood streets, which is why the presence of pedestrians on neighborhood streets without sidewalks and proper traffic control for pedestrians results in the roads being inherently more dangerous than other streets.
