Those things aren't necessarily mutually exclusive. Yes in the US you can be ticketed for jaywalking, but at least in my experience it's more used on busy highways, where you are also endangering drivers who may have to swerve to avoid you. At least within cities I haven't seen it used when crossing a small street when no cars are coming, but it may be different in different places.

Not sure about drivers being at fault, but fault in an accident is a weird concept anyway. For the most part, if you get hit by a car the driver isn't going to suffer serious consequences (they probably won't be convicted of manslaughter, for instance).

But, this whole car centered system we have is pretty screwed up there's no denying that. Something like 50,000 people die in car accidents every year in the US and it's just business as usual.