In my experience, it’s nearly always clear to everyone where they can go while moving traffic around quite efficiently. The UK system seems to either keep pedestrians entirely separate or throw them into the deep end with car-prioritized signaling.
(However, the latter may only be in the city I’m in at the moment, as I at least haven’t seen this in London.)
You mention right of way but it's no comfort to me that I have right of way over a car when the car is trying to push through or running me over!
That seems pretty unavoidable to me, considering we put sidewalks right next to roads. As a pedestrian, I don't want to wait for both directions of traffic to have their turns to cross before I get mine. Though it can be handy if I need to cross diagonally.
Well yeah... because that'd be dangerous if they went at the same time wouldn't it?